Classes

Estimators

GPCCA

class cellrank.tl.estimators.GPCCA(obj, inplace=True, read_from_adata=False, obsp_key=None, g2m_key='G2M_score', s_key='S_score', write_to_adata=True, key=None)[source]

Generalized Perron Cluster Cluster Analysis [Reuter et al., 2018] as implemented in pyGPCCA.

Coarse-grains a discrete Markov chain into a set of macrostates and computes coarse-grained transition probabilities among the macrostates. Each macrostate corresponds to an area of the state space, i.e. to a subset of cells. The assignment is soft, i.e. each cell is assigned to every macrostate with a certain weight, where weights sum to one per cell. Macrostates are computed by maximizing the ‘crispness’ which can be thought of as a measure for minimal overlap between macrostates in a certain inner-product sense. Once the macrostates have been computed, we project the large transition matrix onto a coarse-grained transition matrix among the macrostates via a Galerkin projection. This projection is based on invariant subspaces of the original transition matrix which are obtained using the real Schur decomposition [Reuter et al., 2018].

Parameters
  • obj (Union[KernelExpression, ~AnnData, spmatrix, ndarray]) – Either a cellrank.tl.kernels.Kernel object, an anndata.AnnData object which stores the transition matrix in .obsp attribute or numpy or scipy array.

  • inplace (bool) – Whether to modify adata object inplace or make a copy.

  • read_from_adata (bool) – Whether to read available attributes in adata, if present.

  • obsp_key (Optional[str]) – Key in obj.obsp when obj is an anndata.AnnData object.

  • g2m_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • s_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • write_to_adata (bool) – Whether to write the transition matrix to adata .obsp and the parameters to adata .uns.

  • key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’. Only used when write_to_adata=True.

compute_macrostates(n_states=None, n_cells=30, use_min_chi=False, cluster_key=None, en_cutoff=0.7, p_thresh=1e-15)[source]

Compute the macrostates.

Parameters
  • n_states (Union[int, Tuple[int, int], List[int], Dict[str, int], None]) – Number of macrostates. If None, use the eigengap heuristic.

  • n_cells (Optional[int]) – Number of most likely cells from each macrostate to select.

  • use_min_chi (bool) – Whether to use pygpcca.GPCCA.minChi() to calculate the number of macrostates. If True, n_states corresponds to a closed interval [min, max] inside of which the potentially optimal number of macrostates is searched.

  • cluster_key (Optional[str]) – If a key to cluster labels is given, names and colors of the states will be associated with the clusters.

  • en_cutoff (Optional[float]) – If cluster_key is given, this parameter determines when an approximate recurrent class will be labeled as ‘Unknown’, based on the entropy of the distribution of cells over transcriptomic clusters.

  • p_thresh (float) – If cell cycle scores were provided, a Wilcoxon rank-sum test is conducted to identify cell-cycle states. If the test returns a positive statistic and a p-value smaller than p_thresh, a warning will be issued.

Returns

Nothing, but updates the following fields:

Return type

None

set_terminal_states_from_macrostates(names=None, n_cells=30)[source]

Manually select terminal states from macrostates.

Parameters
  • names (Union[Sequence[str], Mapping[str, str], str, None]) – Names of the macrostates to be marked as terminal. Multiple states can be combined using ‘,’, such as ["Alpha, Beta", "Epsilon"]. If a dict, keys correspond to the names of the macrostates and the values to the new names. If None, select all macrostates.

  • n_cells (int) – Number of most likely cells from each macrostate to select.

Returns

Nothing, just updates the following fields:

Return type

None

compute_terminal_states(method='stability', n_cells=30, alpha=1, stability_threshold=0.96, n_states=None)[source]

Automatically select terminal states from macrostates.

Parameters
  • method (str) –

    One of following:

    • ’eigengap’ - select the number of states based on the eigengap of the transition matrix.

    • ’eigengap_coarse’ - select the number of states based on the eigengap of the diagonal of the coarse-grained transition matrix.

    • ’top_n’ - select top n_states based on the probability of the diagonal of the coarse-grained transition matrix.

    • ’stability’ - select states which have a stability index >= stability_threshold. The stability index is given by the diagonal elements of the coarse-grained transition matrix.

  • n_cells (int) – Number of most likely cells from each macrostate to select.

  • alpha (Optional[float]) – Weight given to the deviation of an eigenvalue from one. Used when method='eigengap' or method='eigengap_coarse'.

  • stability_threshold (float) – Threshold used when method='stability'.

  • n_states (Optional[int]) – Numer of states used when method='top_n'.

Returns

Nothing, just updates the following fields:

Return type

None

compute_gdpt(n_components=10, key_added='gdpt_pseudotime', **kwargs)[source]

Compute generalized Diffusion pseudotime from [Haghverdi et al., 2016] using the real Schur decomposition.

Parameters
  • n_components (int) – Number of real Schur vectors to consider.

  • key_added (str) – Key in adata .obs where to save the pseudotime.

  • kwargs – Keyword arguments for cellrank.tl.GPCCA.compute_schur() if Schur decomposition is not found.

Returns

Nothing, just updates adata .obs[key_added] with the computed pseudotime.

Return type

None

plot_coarse_T(show_stationary_dist=True, show_initial_dist=False, cmap='viridis', xtick_rotation=45, annotate=True, show_cbar=True, title=None, figsize=(8, 8), dpi=80, save=None, text_kwargs=mappingproxy({}), **kwargs)[source]

Plot the coarse-grained transition matrix between macrostates.

Parameters
Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_macrostate_composition(key, width=0.8, title=None, labelrot=45, legend_loc='upper right out', figsize=None, dpi=None, save=None, show=True)[source]

Plot stacked histogram of macrostates over categorical annotations.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • key (str) – Key from adata .obs containing categorical annotations.

  • width (float) – Bar width in [0, 1].

  • title (Optional[str]) – Title of the figure. If None, create one automatically.

  • labelrot (float) – Rotation of labels on x-axis.

  • legend_loc (Optional[str]) – Position of the legend. If None, don’t show legend.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • show (bool) – If False, return matplotlib.pyplot.Axes.

Return type

Optional[Axes]

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

fit(n_lineages=None, cluster_key=None, keys=None, method='krylov', compute_absorption_probabilities=True, **kwargs)[source]

Run the pipeline, computing the macrostates, initial or terminal states and optionally the absorption probabilities.

It is equivalent to running:

if n_lineages is None or n_lineages == 1:
    compute_eigendecomposition(...)  # get the stationary distribution
if n_lineages > 1:
    compute_schur(...)

compute_macrostates(...)

if n_lineages is None:
    compute_terminal_states(...)
else:
    set_terminal_states_from_macrostates(...)

if compute_absorption_probabilities:
    compute_absorption_probabilities(...)
Parameters
  • n_lineages (Optional[int]) – Number of lineages. If None, it will be determined automatically.

  • cluster_key (Optional[str]) – Match computed states against pre-computed clusters to annotate the states. For this, provide a key from adata .obs where cluster labels have been computed.

  • keys (Optional[Sequence[str]]) – Determines which initial or terminal states to use by passing their names. Further, initial or terminal states can be combined. If e.g. the terminal states are [‘Neuronal_1’, ‘Neuronal_1’, ‘Astrocytes’, ‘OPC’], then passing keys=['Neuronal_1, Neuronal_2', 'OPC'] means that the two neuronal terminal states are treated as one and the ‘Astrocyte’ state is excluded.

  • method (str) – Method to use when computing the Schur decomposition. Valid options are: ‘krylov’ or ‘brandts’.

  • compute_absorption_probabilities (bool) – Whether to compute the absorption probabilities or only the initial or terminal states.

  • kwargs – Keyword arguments for cellrank.tl.estimators.GPCCA.compute_macrostates().

Returns

Nothing, just makes available the following fields:

Return type

None

property absorption_probabilities: cellrank.tl._lineage.Lineage

Absorption probabilities.

Return type

Lineage

property adata: anndata._core.anndata.AnnData

Annotated data object.

Returns

Annotated data object.

Return type

anndata.AnnData

property coarse_T: pandas.core.frame.DataFrame

Coarse-grained transition matrix.

Return type

DataFrame

property coarse_initial_distribution: pandas.core.series.Series

Coarse initial distribution.

Return type

Series

property coarse_stationary_distribution: pandas.core.series.Series

Coarse stationary distribution.

Return type

Series

compute_absorption_probabilities(keys=None, check_irreducibility=False, solver='gmres', use_petsc=True, time_to_absorption=None, n_jobs=None, backend='loky', show_progress_bar=True, tol=1e-06, preconditioner=None)

Compute absorption probabilities of a Markov chain.

For each cell, this computes the probability of it reaching any of the approximate recurrent classes defined by terminal_states.

Parameters
  • keys (Optional[Sequence[str]]) – Keys defining the recurrent classes.

  • check_irreducibility (bool) – Check whether the transition matrix is irreducible.

  • solver (str) –

    Solver to use for the linear problem. Options are ‘direct’, ‘gmres’, ‘lgmres’, ‘bicgstab’ or ‘gcrotmk’ when use_petsc=False or one of petsc4py.PETSc.KPS.Type otherwise.

    Information on the scipy iterative solvers can be found in scipy.sparse.linalg() or for petsc4py solver here.

  • use_petsc (bool) – Whether to use solvers from petsc4py or scipy. Recommended for large problems. If no installation is found, defaults to scipy.sparse.linalg.gmres().

  • time_to_absorption (Union[str, Sequence[Union[str, Sequence[str]]], Dict[Union[str, Sequence[str]], str], None]) –

    Whether to compute mean time to absorption and its variance to specific absorbing states.

    If a dict, can be specified as {'Alpha': 'var', ...} to also compute variance. In case when states are a tuple, time to absorption will be computed to the subset of these states, such as [('Alpha', 'Beta'), ...] or {('Alpha', 'Beta'): 'mean', ...}. Can be specified as 'all' to compute it to any absorbing state in keys, which is more efficient than listing all absorbing states.

    It might be beneficial to disable the progress bar as show_progress_bar=False, because many linear systems are being solved.

  • n_jobs (Optional[int]) – Number of parallel jobs to use when using an iterative solver. When use_petsc=True or for quickly-solvable problems, we recommend higher number (>=8) of jobs in order to fully saturate the cores.

  • backend (str) – Which backend to use for multiprocessing. See joblib.Parallel for valid options.

  • show_progress_bar (bool) – Whether to show progress bar when the solver isn’t a direct one.

  • tol (float) – Convergence tolerance for the iterative solver. The default is fine for most cases, only consider decreasing this for severely ill-conditioned matrices.

  • preconditioner (Optional[str]) – Preconditioner to use, only available when use_petsc=True. For available values, see here or the values of petsc4py.PETSc.PC.Type. We recommended ‘ilu’ preconditioner for badly conditioned problems.

Returns

Nothing, but updates the following fields:

  • absorption_probabilities - probabilities of being absorbed into the terminal states.

  • lineage_absorption_times - mean times until absorption to subset absorbing states and optionally their variances saved as '{lineage} mean' and '{lineage} var', respectively, for each subset of absorbing states specified in time_to_absorption.

Return type

None

compute_eigendecomposition(k=20, which='LR', alpha=1, only_evals=False, ncv=None)

Compute eigendecomposition of transition matrix.

Uses a sparse implementation, if possible, and only computes the top \(k\) eigenvectors to speed up the computation. Computes both left and right eigenvectors.

Parameters
  • k (int) – Number of eigenvalues/vectors to compute.

  • which (str) – Eigenvalues are in general complex. ‘LR’ - largest real part, ‘LM’ - largest magnitude.

  • alpha (float) – Used to compute the eigengap. alpha is the weight given to the deviation of an eigenvalue from one.

  • only_evals (bool) – Compute only eigenvalues.

  • ncv (Optional[int]) – Number of Lanczos vectors generated.

Returns

Nothing, but updates the following field:

Return type

None

compute_lineage_drivers(lineages=None, method='fischer', cluster_key=None, clusters=None, layer='X', use_raw=False, confidence_level=0.95, n_perms=1000, seed=None, return_drivers=True, **kwargs)

Compute driver genes per lineage.

Correlates gene expression with lineage probabilities, for a given lineage and set of clusters. Often, it makes sense to restrict this to a set of clusters which are relevant for the specified lineages.

Parameters
  • lineages (Union[str, Sequence, None]) – Either a set of lineage names from absorption_probabilities .names or None, in which case all lineages are considered.

  • method (str) –

    Mode to use when calculating p-values and confidence intervals. Valid options are:

    • ’fischer’ - use Fischer transformation [Fisher, 1921].

    • ’perm_test’ - use permutation test.

  • cluster_key (Optional[str]) – Key from adata .obs to obtain cluster annotations. These are considered for clusters.

  • clusters (Union[str, Sequence, None]) – Restrict the correlations to these clusters.

  • layer (str) – Key from adata .layers.

  • use_raw (bool) – Whether or not to use adata .raw to correlate gene expression. If using a layer other than .X, this must be set to False.

  • confidence_level (float) – Confidence level for the confidence interval calculation. Must be in [0, 1].

  • n_perms (int) – Number of permutations to use when method='perm_test'.

  • seed (Optional[int]) – Random seed when method='perm_test'.

  • return_drivers (bool) – Whether to return the drivers. This also contains the lower and upper confidence_level confidence interval bounds.

  • show_progress_bar – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend – Which backend to use for parallelization. See joblib.Parallel for valid options.

Return type

Optional[DataFrame]

Returns

  • Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, 1 for each lineage –

    • {lineage} corr - correlation between the gene expression and absorption probabilities.

    • {lineage} pval - calculated p-values for double-sided test.

    • {lineage} qval - corrected p-values using Benjamini-Hochberg method at level 0.05.

    • {lineage} ci low - lower bound of the confidence_level correlation confidence interval.

    • {lineage} ci high - upper bound of the confidence_level correlation confidence interval.

  • Only if return_drivers=True.

  • Otherwise, updates adata .var or adata .raw.var, depending use_raw with –

    • '{direction} {lineage} corr' - the potential lineage drivers.

    • '{direction} {lineage} qval' - the corrected p-values.

  • Also updates the following fields

compute_lineage_priming(method='kl_divergence', early_cells=None)

Compute the degree of lineage priming.

This method computes how naive vs. committed each individual cell is. It returns a score where 0 stands for naive and 1 stands for committed.

Parameters
  • method (Literal[‘kl_divergence’, ‘entropy’]) –

    The method used to compute the degree of lineage priming. Valid options are:

    • ’kl_divergence’: as in [Velten et al., 2017], computes KL-divergence between the fate probabilities of a cell and the average fate probabilities. Computation of average fate probabilities can be restricted to a set of user-defined early_cells.

    • ’entropy’: as in [Setty et al., 2019], computes entropy over a cell’s fate probabilities.

  • early_cells (Union[Mapping[str, Sequence[str]], Sequence[str], None]) – Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. If a dict, the key species a cluster key in anndata.AnnData.obs and the values specify cluster labels containing early cells.

Returns

Return type

The priming degree.

compute_partition()

Compute communication classes for the Markov chain.

Returns

Nothing, but updates the following fields:

Return type

None

compute_schur(n_components=10, initial_distribution=None, method='krylov', which='LR', alpha=1)

Compute the Schur decomposition.

Parameters
  • n_components (int) – Number of vectors to compute.

  • initial_distribution (Optional[ndarray]) – Input probability distribution over all cells. If None, uniform is chosen.

  • method (str) –

    Method for calculating the Schur vectors. Valid options are: ‘krylov’ or ‘brandts’. For benefits of each method, see pygpcca.GPCCA.

    The former is an iterative procedure that computes a partial, sorted Schur decomposition for large, sparse matrices whereas the latter computes a full sorted Schur decomposition of a dense matrix.

  • which (str) – Eigenvalues are in general complex. ‘LR’ - largest real part, ‘LM’ - largest magnitude.

  • alpha (float) – Used to compute the eigengap. alpha is the weight given to the deviation of an eigenvalue from one.

Returns

Nothing, but updates the following fields:

Return type

None

copy()

Return a copy of self, including the underlying adata object.

Return type

BaseEstimator

property eigendecomposition: Mapping[str, Any]

Eigendecomposition.

Return type

Mapping[str, Any]

property is_irreducible

Whether the Markov chain is irreducible or not.

property issparse: bool

Whether the transition matrix is sparse or not.

Return type

bool

property kernel: cellrank.tl.kernels._base_kernel.KernelExpression

Underlying kernel.

Return type

KernelExpression

property lineage_absorption_times: pandas.core.frame.DataFrame

Lineage absorption times.

Return type

DataFrame

property lineage_drivers: pandas.core.frame.DataFrame

Lineage drivers.

Return type

DataFrame

property macrostates: pandas.core.series.Series

Macrostates.

Return type

Series

property macrostates_memberships: cellrank.tl._lineage.Lineage

Macrostates memberships.

Return type

Lineage

plot_absorption_probabilities(data, prop, discrete=False, lineages=None, cluster_key=None, mode='embedding', time_key='latent_time', title=None, same_plot=False, cmap='viridis', **kwargs)

Plot discrete states or probabilities in an embedding.

Parameters
  • discrete (bool) – Whether to plot in discrete or continuous mode.

  • lineages (Union[str, Sequence[str], None]) – Plot only these lineages. If None, plot all lineages.

  • cluster_key (Optional[str]) – Key from adata .obs for plotting categorical observations.

  • mode (str) –

    Can be either ‘embedding’ or ‘time’:

    • ’embedding’ - plot the embedding while coloring in the absorption probabilities.

    • ’time’ - plot the pseudotime on x-axis and the absorption probabilities on y-axis.

  • time_key (str) – Key from adata .obs to use as a pseudotime ordering of the cells.

  • title (Optional[str]) – Either None, in which case titles are '{to,from} {terminal,initial} {state}', or an array of titles, one per lineage.

  • same_plot (bool) – Whether to plot the lineages on the same plot using color gradients when mode='embedding'.

  • cmap (Union[str, ListedColormap]) – Colormap to use.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_eigendecomposition(left=False, *args, **kwargs)

Plot eigenvectors in an embedding.

Parameters
  • left (bool) – Whether to plot left or right eigenvectors.

  • use – Which or how many vectors are to be plotted.

  • abs_value – Whether to take the absolute value before plotting.

  • cluster_key – Key in adata .obs for plotting categorical observations.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_lineage_drivers(lineage, n_genes=8, ncols=None, use_raw=False, title_fmt='{gene} qval={qval:.4e}', figsize=None, dpi=None, save=None, **kwargs)

Plot lineage drivers discovered by compute_lineage_drivers().

Parameters
  • lineage (str) – Lineage for which to plot the driver genes.

  • n_genes (int) – Top most correlated genes to plot.

  • ncols (Optional[int]) – Number of columns.

  • use_raw (bool) – Whether to look in adata .raw.var or adata .var.

  • title_fmt (str) – Title format. Possible keywords include {gene}, {qval}, {corr} for gene name, q-value and correlation, respectively.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_lineage_drivers_correlation(lineage_x, lineage_y, color=None, gene_sets=None, gene_sets_colors=None, use_raw=False, cmap='RdYlBu_r', fontsize=12, adjust_text=False, legend_loc='best', figsize=(4, 4), dpi=None, save=None, show=True, **kwargs)

Show scatter plot of gene-correlations between two lineages.

Optionally, you can pass a dict of gene names that will be annotated in the plot.

Parameters
  • lineage_x (str) – Name of the lineage on the x-axis.

  • lineage_y (str) – Name of the lineage on the y-axis.

  • color (Optional[str]) – Key in adata .var.

  • gene_sets (Optional[Dict[str, Iterable]]) – Gene sets annotations of the form {‘gene_set_name’: [‘gene_1’, ‘gene_2’], …}.

  • gene_sets_colors (Optional[Iterable]) – List of colors where each entry corresponds to a gene set from genes_sets. If None and keys in gene_sets correspond to lineage names, use the lineage colors. Otherwise, use default colors.

  • use_raw (bool) – Whether to access adata .raw.var or adata .var.

  • cmap (str) – Colormap to use.

  • fontsize (int) – Size of the text when plotting gene_sets.

  • adjust_text (bool) – Whether to automatically adjust text in order to reduce overlap.

  • legend_loc (Optional[str]) – Position of the legend. If None, don’t show the legend. Only used when gene_sets!=None.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • show (bool) – If False, return matplotlib.pyplot.Axes.

  • kwargs (Any) – Keyword arguments for scanpy.pl.scatter().

Return type

Optional[Axes]

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

Notes

This plot is based on the following notebook by Maren Büttner.

plot_macrostates(data, prop, discrete=False, lineages=None, cluster_key=None, mode='embedding', time_key='latent_time', title=None, same_plot=False, cmap='viridis', **kwargs)

Plot discrete states or probabilities in an embedding.

Parameters
  • discrete (bool) – Whether to plot in discrete or continuous mode.

  • lineages (Union[str, Sequence[str], None]) – Plot only these lineages. If None, plot all lineages.

  • cluster_key (Optional[str]) – Key from adata .obs for plotting categorical observations.

  • mode (str) –

    Can be either ‘embedding’ or ‘time’:

    • ’embedding’ - plot the embedding while coloring in the absorption probabilities.

    • ’time’ - plot the pseudotime on x-axis and the absorption probabilities on y-axis.

  • time_key (str) – Key from adata .obs to use as a pseudotime ordering of the cells.

  • title (Optional[str]) – Either None, in which case titles are '{to,from} {terminal,initial} {state}', or an array of titles, one per lineage.

  • same_plot (bool) – Whether to plot the lineages on the same plot using color gradients when mode='embedding'.

  • cmap (Union[str, ListedColormap]) – Colormap to use.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_schur(vectors, prop, use=None, abs_value=False, cluster_key=None, **kwargs)

Plot vectors in an embedding.

Parameters
  • use (Union[int, Tuple[int], List[int], None]) – Which or how many vectors are to be plotted.

  • abs_value (bool) – Whether to take the absolute value before plotting.

  • cluster_key (Optional[str]) – Key in adata .obs for plotting categorical observations.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_schur_matrix(title='schur matrix', cmap='viridis', figsize=None, dpi=80, save=None, **kwargs)

Plot the Schur matrix.

Parameters
Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_spectrum(n=None, real_only=False, show_eigengap=True, show_all_xticks=True, legend_loc=None, title=None, figsize=(5, 5), dpi=100, save=None, marker='.', **kwargs)

Plot the top eigenvalues in real or complex plane.

Parameters
  • n (Optional[int]) – Number of eigenvalues to show. If None, show all that have been computed.

  • real_only (bool) – Whether to plot only the real part of the spectrum.

  • show_eigengap (bool) – When real_only=True, this determines whether to show the inferred eigengap as a dotted line.

  • show_all_xticks (bool) – When real_only=True, this determines whether to show the indices of all eigenvalues on the x-axis.

  • legend_loc (Optional[str]) – Location parameter for the legend.

  • title (Optional[str]) – Title of the figure.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (int) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • marker (str) – Marker symbol used, valid options can be found in matplotlib.markers.

  • kwargs – Keyword arguments for matplotlib.pyplot.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_terminal_states(data, prop, discrete=False, lineages=None, cluster_key=None, mode='embedding', time_key='latent_time', title=None, same_plot=False, cmap='viridis', **kwargs)

Plot discrete states or probabilities in an embedding.

Parameters
  • discrete (bool) – Whether to plot in discrete or continuous mode.

  • lineages (Union[str, Sequence[str], None]) – Plot only these lineages. If None, plot all lineages.

  • cluster_key (Optional[str]) – Key from adata .obs for plotting categorical observations.

  • mode (str) –

    Can be either ‘embedding’ or ‘time’:

    • ’embedding’ - plot the embedding while coloring in the absorption probabilities.

    • ’time’ - plot the pseudotime on x-axis and the absorption probabilities on y-axis.

  • time_key (str) – Key from adata .obs to use as a pseudotime ordering of the cells.

  • title (Optional[str]) – Either None, in which case titles are '{to,from} {terminal,initial} {state}', or an array of titles, one per lineage.

  • same_plot (bool) – Whether to plot the lineages on the same plot using color gradients when mode='embedding'.

  • cmap (Union[str, ListedColormap]) – Colormap to use.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

property priming_degree: pandas.core.series.Series

Priming degree.

Return type

Series

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property recurrent_classes

Recurrent classes of the Markov chain.

rename_terminal_states(new_names, update_adata=True)

Rename the names of terminal_states.

Parameters
  • new_names (Mapping[str, str]) – Mapping where keys are the old names and the values are the new names. New names must be unique.

  • update_adata (bool) – Whether to update underlying adata object as well or not.

Returns

Nothing, just updates the names of terminal_states.

Return type

None

property schur: numpy.ndarray

Schur vectors.

Return type

ndarray

property schur_matrix: numpy.ndarray

Schur matrix.

Return type

ndarray

set_terminal_states(labels, cluster_key=None, en_cutoff=None, p_thresh=None, add_to_existing=False, **kwargs)

Manually define terminal states.

Parameters
  • labels (Union[Series, Dict[str, Sequence[Any]]]) –

    Defines the terminal states. Valid options are:

    • categorical pandas.Series where each category corresponds to one terminal state. NaN entries denote cells that do not belong to any terminal state, i.e. these are either initial or transient cells.

    • dict where keys are terminal states and values are lists of cell barcodes corresponding to annotations in adata .obs_names. If only 1 key is provided, values should correspond to terminal state clusters if a categorical pandas.Series can be found in adata .obs.

  • cluster_key (Optional[str]) – Key from adata.obs where categorical cluster labels are stored. These are used to associate names and colors with each terminal state. Each terminal state will be given the name and color corresponding to the cluster it mostly overlaps with.

  • en_cutoff (Optional[float]) – If cluster_key is given, this parameter determines when an approximate recurrent class will be labeled as ‘Unknown’, based on the entropy of the distribution of cells over transcriptomic clusters.

  • p_thresh (Optional[float]) – If cell cycle scores were provided, a Wilcoxon rank-sum test is conducted to identify cell-cycle states. If the test returns a positive statistic and a p-value smaller than p_thresh, a warning will be issued.

  • add_to_existing (bool) – Whether the new terminal states should be added to pre-existing ones. Cells already assigned to a terminal state will be re-assigned to the new terminal state if there’s a conflict between old and new annotations. This throws an error if no previous annotations corresponding to terminal states have been found.

Returns

Nothing, but updates the following fields:

Return type

None

property terminal_states: pandas.core.series.Series

Terminal states.

Return type

Series

property terminal_states_probabilities: pandas.core.series.Series

Terminal states probabilities.

Return type

Series

property transient_classes

Transient classes of the Markov chain.

property transition_matrix: Union[numpy.ndarray, scipy.sparse.base.spmatrix]

Transition matrix.

Return type

Union[ndarray, spmatrix]

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

CFLARE

class cellrank.tl.estimators.CFLARE(obj, inplace=True, read_from_adata=False, obsp_key=None, g2m_key='G2M_score', s_key='S_score', write_to_adata=True, key=None)[source]

Compute the initial/terminal states of a Markov chain via spectral heuristics.

This estimator uses the left eigenvectors of the transition matrix to filter to a set of recurrent cells and the right eigenvectors to cluster this set of cells into discrete groups.

Parameters
  • obj (Union[KernelExpression, ~AnnData, spmatrix, ndarray]) – Either a cellrank.tl.kernels.Kernel object, an anndata.AnnData object which stores the transition matrix in .obsp attribute or numpy or scipy array.

  • inplace (bool) – Whether to modify adata object inplace or make a copy.

  • read_from_adata (bool) – Whether to read available attributes in adata, if present.

  • obsp_key (Optional[str]) – Key in obj.obsp when obj is an anndata.AnnData object.

  • g2m_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • s_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • write_to_adata (bool) – Whether to write the transition matrix to adata .obsp and the parameters to adata .uns.

  • key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’. Only used when write_to_adata=True.

compute_terminal_states(use=None, percentile=98, method='kmeans', cluster_key=None, n_clusters_kmeans=None, n_neighbors=20, resolution=0.1, n_matches_min=0, n_neighbors_filtering=15, basis=None, n_comps=5, scale=False, en_cutoff=0.7, p_thresh=1e-15)[source]

Find approximate recurrent classes of the Markov chain.

Filter to obtain recurrent states in left eigenvectors. Cluster to obtain approximate recurrent classes in right eigenvectors.

Parameters
  • use (Union[int, Tuple[int], List[int], range, None]) – Which or how many first eigenvectors to use as features for clustering/filtering. If None, use the eigengap statistic.

  • percentile (Optional[int]) – Threshold used for filtering out cells which are most likely transient states. Cells which are in the lower percentile percent of each eigenvector will be removed from the data matrix.

  • method (str) – Method to be used for clustering. Must be one of ‘louvain’, ‘leiden’ or ‘kmeans’.

  • cluster_key (Optional[str]) – If a key to cluster labels is given, terminal_states will get associated with these for naming and colors.

  • n_clusters_kmeans (Optional[int]) – If None, this is set to use + 1.

  • n_neighbors (int) – If we use ‘louvain’ or ‘leiden’ for clustering cells, we need to build a KNN graph. This is the \(K\) parameter for that, the number of neighbors for each cell.

  • resolution (float) – Resolution parameter for ‘louvain’ or ‘leiden’ clustering. Should be chosen relatively small.

  • n_matches_min (Optional[int]) – Filters out cells which don’t have at least n_matches_min neighbors from the same class. This filters out some cells which are transient but have been misassigned.

  • n_neighbors_filtering (int) – Parameter for filtering cells. Cells are filtered out if they don’t have at least n_matches_min neighbors among their n_neighbors_filtering nearest cells.

  • basis (Optional[str]) – Key from :paramref`adata` .obsm to be used as additional features for the clustering.

  • n_comps (int) – Number of embedding components to be use when basis is not None.

  • scale (bool) – Scale to z-scores. Consider using this if appending embedding to features.

  • en_cutoff (Optional[float]) – If cluster_key is given, this parameter determines when an approximate recurrent class will be labeled as ‘Unknown’, based on the entropy of the distribution of cells over transcriptomic clusters.

  • p_thresh (float) – If cell cycle scores were provided, a Wilcoxon rank-sum test is conducted to identify cell-cycle states. If the test returns a positive statistic and a p-value smaller than p_thresh, a warning will be issued.

Returns

Nothing, but updates the following fields:

Return type

None

fit(n_lineages, keys=None, cluster_key=None, compute_absorption_probabilities=True, **kwargs)[source]

Run the pipeline, computing the initial or terminal states and optionally the absorption probabilities.

It is equivalent to running:

compute_eigendecomposition(...)
compute_terminal_states(...)
compute_absorption_probabilities(...)
Parameters
  • n_lineages (Optional[int]) – Number of lineages. If None, it will be determined automatically.

  • cluster_key (Optional[str]) – Match computed states against pre-computed clusters to annotate the states. For this, provide a key from adata .obs where cluster labels have been computed.

  • keys (Optional[Sequence[str]]) – Determines which initial or terminal states to use by passing their names. Further, initial or terminal states can be combined. If e.g. the terminal states are [‘Neuronal_1’, ‘Neuronal_1’, ‘Astrocytes’, ‘OPC’], then passing keys=['Neuronal_1, Neuronal_2', 'OPC'] means that the two neuronal terminal states are treated as one and the ‘Astrocyte’ state is excluded.

  • kwargs – Keyword arguments for compute_terminal_states(), such as n_cells.

Returns

Nothing, just makes available the following fields:

Return type

None

property absorption_probabilities: cellrank.tl._lineage.Lineage

Absorption probabilities.

Return type

Lineage

property adata: anndata._core.anndata.AnnData

Annotated data object.

Returns

Annotated data object.

Return type

anndata.AnnData

compute_absorption_probabilities(keys=None, check_irreducibility=False, solver='gmres', use_petsc=True, time_to_absorption=None, n_jobs=None, backend='loky', show_progress_bar=True, tol=1e-06, preconditioner=None)

Compute absorption probabilities of a Markov chain.

For each cell, this computes the probability of it reaching any of the approximate recurrent classes defined by terminal_states.

Parameters
  • keys (Optional[Sequence[str]]) – Keys defining the recurrent classes.

  • check_irreducibility (bool) – Check whether the transition matrix is irreducible.

  • solver (str) –

    Solver to use for the linear problem. Options are ‘direct’, ‘gmres’, ‘lgmres’, ‘bicgstab’ or ‘gcrotmk’ when use_petsc=False or one of petsc4py.PETSc.KPS.Type otherwise.

    Information on the scipy iterative solvers can be found in scipy.sparse.linalg() or for petsc4py solver here.

  • use_petsc (bool) – Whether to use solvers from petsc4py or scipy. Recommended for large problems. If no installation is found, defaults to scipy.sparse.linalg.gmres().

  • time_to_absorption (Union[str, Sequence[Union[str, Sequence[str]]], Dict[Union[str, Sequence[str]], str], None]) –

    Whether to compute mean time to absorption and its variance to specific absorbing states.

    If a dict, can be specified as {'Alpha': 'var', ...} to also compute variance. In case when states are a tuple, time to absorption will be computed to the subset of these states, such as [('Alpha', 'Beta'), ...] or {('Alpha', 'Beta'): 'mean', ...}. Can be specified as 'all' to compute it to any absorbing state in keys, which is more efficient than listing all absorbing states.

    It might be beneficial to disable the progress bar as show_progress_bar=False, because many linear systems are being solved.

  • n_jobs (Optional[int]) – Number of parallel jobs to use when using an iterative solver. When use_petsc=True or for quickly-solvable problems, we recommend higher number (>=8) of jobs in order to fully saturate the cores.

  • backend (str) – Which backend to use for multiprocessing. See joblib.Parallel for valid options.

  • show_progress_bar (bool) – Whether to show progress bar when the solver isn’t a direct one.

  • tol (float) – Convergence tolerance for the iterative solver. The default is fine for most cases, only consider decreasing this for severely ill-conditioned matrices.

  • preconditioner (Optional[str]) – Preconditioner to use, only available when use_petsc=True. For available values, see here or the values of petsc4py.PETSc.PC.Type. We recommended ‘ilu’ preconditioner for badly conditioned problems.

Returns

Nothing, but updates the following fields:

  • absorption_probabilities - probabilities of being absorbed into the terminal states.

  • lineage_absorption_times - mean times until absorption to subset absorbing states and optionally their variances saved as '{lineage} mean' and '{lineage} var', respectively, for each subset of absorbing states specified in time_to_absorption.

Return type

None

compute_eigendecomposition(k=20, which='LR', alpha=1, only_evals=False, ncv=None)

Compute eigendecomposition of transition matrix.

Uses a sparse implementation, if possible, and only computes the top \(k\) eigenvectors to speed up the computation. Computes both left and right eigenvectors.

Parameters
  • k (int) – Number of eigenvalues/vectors to compute.

  • which (str) – Eigenvalues are in general complex. ‘LR’ - largest real part, ‘LM’ - largest magnitude.

  • alpha (float) – Used to compute the eigengap. alpha is the weight given to the deviation of an eigenvalue from one.

  • only_evals (bool) – Compute only eigenvalues.

  • ncv (Optional[int]) – Number of Lanczos vectors generated.

Returns

Nothing, but updates the following field:

Return type

None

compute_lineage_drivers(lineages=None, method='fischer', cluster_key=None, clusters=None, layer='X', use_raw=False, confidence_level=0.95, n_perms=1000, seed=None, return_drivers=True, **kwargs)

Compute driver genes per lineage.

Correlates gene expression with lineage probabilities, for a given lineage and set of clusters. Often, it makes sense to restrict this to a set of clusters which are relevant for the specified lineages.

Parameters
  • lineages (Union[str, Sequence, None]) – Either a set of lineage names from absorption_probabilities .names or None, in which case all lineages are considered.

  • method (str) –

    Mode to use when calculating p-values and confidence intervals. Valid options are:

    • ’fischer’ - use Fischer transformation [Fisher, 1921].

    • ’perm_test’ - use permutation test.

  • cluster_key (Optional[str]) – Key from adata .obs to obtain cluster annotations. These are considered for clusters.

  • clusters (Union[str, Sequence, None]) – Restrict the correlations to these clusters.

  • layer (str) – Key from adata .layers.

  • use_raw (bool) – Whether or not to use adata .raw to correlate gene expression. If using a layer other than .X, this must be set to False.

  • confidence_level (float) – Confidence level for the confidence interval calculation. Must be in [0, 1].

  • n_perms (int) – Number of permutations to use when method='perm_test'.

  • seed (Optional[int]) – Random seed when method='perm_test'.

  • return_drivers (bool) – Whether to return the drivers. This also contains the lower and upper confidence_level confidence interval bounds.

  • show_progress_bar – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend – Which backend to use for parallelization. See joblib.Parallel for valid options.

Return type

Optional[DataFrame]

Returns

  • Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, 1 for each lineage –

    • {lineage} corr - correlation between the gene expression and absorption probabilities.

    • {lineage} pval - calculated p-values for double-sided test.

    • {lineage} qval - corrected p-values using Benjamini-Hochberg method at level 0.05.

    • {lineage} ci low - lower bound of the confidence_level correlation confidence interval.

    • {lineage} ci high - upper bound of the confidence_level correlation confidence interval.

  • Only if return_drivers=True.

  • Otherwise, updates adata .var or adata .raw.var, depending use_raw with –

    • '{direction} {lineage} corr' - the potential lineage drivers.

    • '{direction} {lineage} qval' - the corrected p-values.

  • Also updates the following fields

compute_lineage_priming(method='kl_divergence', early_cells=None)

Compute the degree of lineage priming.

This method computes how naive vs. committed each individual cell is. It returns a score where 0 stands for naive and 1 stands for committed.

Parameters
  • method (Literal[‘kl_divergence’, ‘entropy’]) –

    The method used to compute the degree of lineage priming. Valid options are:

    • ’kl_divergence’: as in [Velten et al., 2017], computes KL-divergence between the fate probabilities of a cell and the average fate probabilities. Computation of average fate probabilities can be restricted to a set of user-defined early_cells.

    • ’entropy’: as in [Setty et al., 2019], computes entropy over a cell’s fate probabilities.

  • early_cells (Union[Mapping[str, Sequence[str]], Sequence[str], None]) – Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. If a dict, the key species a cluster key in anndata.AnnData.obs and the values specify cluster labels containing early cells.

Returns

Return type

The priming degree.

compute_partition()

Compute communication classes for the Markov chain.

Returns

Nothing, but updates the following fields:

Return type

None

copy()

Return a copy of self, including the underlying adata object.

Return type

BaseEstimator

property eigendecomposition: Mapping[str, Any]

Eigendecomposition.

Return type

Mapping[str, Any]

property is_irreducible

Whether the Markov chain is irreducible or not.

property issparse: bool

Whether the transition matrix is sparse or not.

Return type

bool

property kernel: cellrank.tl.kernels._base_kernel.KernelExpression

Underlying kernel.

Return type

KernelExpression

property lineage_absorption_times: pandas.core.frame.DataFrame

Lineage absorption times.

Return type

DataFrame

property lineage_drivers: pandas.core.frame.DataFrame

Lineage drivers.

Return type

DataFrame

plot_absorption_probabilities(data, prop, discrete=False, lineages=None, cluster_key=None, mode='embedding', time_key='latent_time', title=None, same_plot=False, cmap='viridis', **kwargs)

Plot discrete states or probabilities in an embedding.

Parameters
  • discrete (bool) – Whether to plot in discrete or continuous mode.

  • lineages (Union[str, Sequence[str], None]) – Plot only these lineages. If None, plot all lineages.

  • cluster_key (Optional[str]) – Key from adata .obs for plotting categorical observations.

  • mode (str) –

    Can be either ‘embedding’ or ‘time’:

    • ’embedding’ - plot the embedding while coloring in the absorption probabilities.

    • ’time’ - plot the pseudotime on x-axis and the absorption probabilities on y-axis.

  • time_key (str) – Key from adata .obs to use as a pseudotime ordering of the cells.

  • title (Optional[str]) – Either None, in which case titles are '{to,from} {terminal,initial} {state}', or an array of titles, one per lineage.

  • same_plot (bool) – Whether to plot the lineages on the same plot using color gradients when mode='embedding'.

  • cmap (Union[str, ListedColormap]) – Colormap to use.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_eigendecomposition(left=False, *args, **kwargs)

Plot eigenvectors in an embedding.

Parameters
  • left (bool) – Whether to plot left or right eigenvectors.

  • use – Which or how many vectors are to be plotted.

  • abs_value – Whether to take the absolute value before plotting.

  • cluster_key – Key in adata .obs for plotting categorical observations.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_lineage_drivers(lineage, n_genes=8, ncols=None, use_raw=False, title_fmt='{gene} qval={qval:.4e}', figsize=None, dpi=None, save=None, **kwargs)

Plot lineage drivers discovered by compute_lineage_drivers().

Parameters
  • lineage (str) – Lineage for which to plot the driver genes.

  • n_genes (int) – Top most correlated genes to plot.

  • ncols (Optional[int]) – Number of columns.

  • use_raw (bool) – Whether to look in adata .raw.var or adata .var.

  • title_fmt (str) – Title format. Possible keywords include {gene}, {qval}, {corr} for gene name, q-value and correlation, respectively.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_lineage_drivers_correlation(lineage_x, lineage_y, color=None, gene_sets=None, gene_sets_colors=None, use_raw=False, cmap='RdYlBu_r', fontsize=12, adjust_text=False, legend_loc='best', figsize=(4, 4), dpi=None, save=None, show=True, **kwargs)

Show scatter plot of gene-correlations between two lineages.

Optionally, you can pass a dict of gene names that will be annotated in the plot.

Parameters
  • lineage_x (str) – Name of the lineage on the x-axis.

  • lineage_y (str) – Name of the lineage on the y-axis.

  • color (Optional[str]) – Key in adata .var.

  • gene_sets (Optional[Dict[str, Iterable]]) – Gene sets annotations of the form {‘gene_set_name’: [‘gene_1’, ‘gene_2’], …}.

  • gene_sets_colors (Optional[Iterable]) – List of colors where each entry corresponds to a gene set from genes_sets. If None and keys in gene_sets correspond to lineage names, use the lineage colors. Otherwise, use default colors.

  • use_raw (bool) – Whether to access adata .raw.var or adata .var.

  • cmap (str) – Colormap to use.

  • fontsize (int) – Size of the text when plotting gene_sets.

  • adjust_text (bool) – Whether to automatically adjust text in order to reduce overlap.

  • legend_loc (Optional[str]) – Position of the legend. If None, don’t show the legend. Only used when gene_sets!=None.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • show (bool) – If False, return matplotlib.pyplot.Axes.

  • kwargs (Any) – Keyword arguments for scanpy.pl.scatter().

Return type

Optional[Axes]

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

Notes

This plot is based on the following notebook by Maren Büttner.

plot_spectrum(n=None, real_only=False, show_eigengap=True, show_all_xticks=True, legend_loc=None, title=None, figsize=(5, 5), dpi=100, save=None, marker='.', **kwargs)

Plot the top eigenvalues in real or complex plane.

Parameters
  • n (Optional[int]) – Number of eigenvalues to show. If None, show all that have been computed.

  • real_only (bool) – Whether to plot only the real part of the spectrum.

  • show_eigengap (bool) – When real_only=True, this determines whether to show the inferred eigengap as a dotted line.

  • show_all_xticks (bool) – When real_only=True, this determines whether to show the indices of all eigenvalues on the x-axis.

  • legend_loc (Optional[str]) – Location parameter for the legend.

  • title (Optional[str]) – Title of the figure.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (int) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • marker (str) – Marker symbol used, valid options can be found in matplotlib.markers.

  • kwargs – Keyword arguments for matplotlib.pyplot.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_terminal_states(data, prop, discrete=False, lineages=None, cluster_key=None, mode='embedding', time_key='latent_time', title=None, same_plot=False, cmap='viridis', **kwargs)

Plot discrete states or probabilities in an embedding.

Parameters
  • discrete (bool) – Whether to plot in discrete or continuous mode.

  • lineages (Union[str, Sequence[str], None]) – Plot only these lineages. If None, plot all lineages.

  • cluster_key (Optional[str]) – Key from adata .obs for plotting categorical observations.

  • mode (str) –

    Can be either ‘embedding’ or ‘time’:

    • ’embedding’ - plot the embedding while coloring in the absorption probabilities.

    • ’time’ - plot the pseudotime on x-axis and the absorption probabilities on y-axis.

  • time_key (str) – Key from adata .obs to use as a pseudotime ordering of the cells.

  • title (Optional[str]) – Either None, in which case titles are '{to,from} {terminal,initial} {state}', or an array of titles, one per lineage.

  • same_plot (bool) – Whether to plot the lineages on the same plot using color gradients when mode='embedding'.

  • cmap (Union[str, ListedColormap]) – Colormap to use.

  • basis – Basis to use when mode='embedding'. If None, use ‘umap’.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

property priming_degree: pandas.core.series.Series

Priming degree.

Return type

Series

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property recurrent_classes

Recurrent classes of the Markov chain.

rename_terminal_states(new_names, update_adata=True)

Rename the names of terminal_states.

Parameters
  • new_names (Mapping[str, str]) – Mapping where keys are the old names and the values are the new names. New names must be unique.

  • update_adata (bool) – Whether to update underlying adata object as well or not.

Returns

Nothing, just updates the names of terminal_states.

Return type

None

set_terminal_states(labels, cluster_key=None, en_cutoff=None, p_thresh=None, add_to_existing=False, **kwargs)

Manually define terminal states.

Parameters
  • labels (Union[Series, Dict[str, Sequence[Any]]]) –

    Defines the terminal states. Valid options are:

    • categorical pandas.Series where each category corresponds to one terminal state. NaN entries denote cells that do not belong to any terminal state, i.e. these are either initial or transient cells.

    • dict where keys are terminal states and values are lists of cell barcodes corresponding to annotations in adata .obs_names. If only 1 key is provided, values should correspond to terminal state clusters if a categorical pandas.Series can be found in adata .obs.

  • cluster_key (Optional[str]) – Key from adata.obs where categorical cluster labels are stored. These are used to associate names and colors with each terminal state. Each terminal state will be given the name and color corresponding to the cluster it mostly overlaps with.

  • en_cutoff (Optional[float]) – If cluster_key is given, this parameter determines when an approximate recurrent class will be labeled as ‘Unknown’, based on the entropy of the distribution of cells over transcriptomic clusters.

  • p_thresh (Optional[float]) – If cell cycle scores were provided, a Wilcoxon rank-sum test is conducted to identify cell-cycle states. If the test returns a positive statistic and a p-value smaller than p_thresh, a warning will be issued.

  • add_to_existing (bool) – Whether the new terminal states should be added to pre-existing ones. Cells already assigned to a terminal state will be re-assigned to the new terminal state if there’s a conflict between old and new annotations. This throws an error if no previous annotations corresponding to terminal states have been found.

Returns

Nothing, but updates the following fields:

Return type

None

property terminal_states: pandas.core.series.Series

Terminal states.

Return type

Series

property terminal_states_probabilities: pandas.core.series.Series

Terminal states probabilities.

Return type

Series

property transient_classes

Transient classes of the Markov chain.

property transition_matrix: Union[numpy.ndarray, scipy.sparse.base.spmatrix]

Transition matrix.

Return type

Union[ndarray, spmatrix]

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

Kernels

Velocity Kernel

class cellrank.tl.kernels.VelocityKernel(adata, backward=False, vkey='velocity', xkey='Ms', gene_subset=None, compute_cond_num=False, check_connectivity=False, **kwargs)[source]

Kernel which computes a transition matrix based on RNA velocity.

This borrows ideas from both [La Manno et al., 2018] and [Bergen et al., 2020]. In short, for each cell i, we compute transition probabilities \(p_{i, j}\) to each cell j in the neighborhood of i. The transition probabilities are computed as a multinomial logistic regression where the weights \(w_j\) (for all j) are given by the vector that connects cell i with cell j in gene expression space, and the features \(x_i\) are given by the velocity vector \(v_i\) of cell i.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • vkey (str) – Key in adata .uns where the velocities are stored.

  • xkey (str) – Key in adata .layers where expected gene expression counts are stored.

  • gene_subset (Optional[Iterable]) – List of genes to be used to compute transition probabilities. By default, genes from adata .var['velocity_genes'] are used.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • check_connectivity (bool) – Check whether the underlying KNN graph is connected.

  • kwargs (Any) – Keyword arguments for cellrank.tl.kernels.Kernel.

compute_transition_matrix(mode='deterministic', backward_mode='transpose', scheme='correlation', softmax_scale=None, n_samples=1000, seed=None, check_irreducibility=False, **kwargs)[source]

Compute transition matrix based on velocity directions on the local manifold.

For each cell, infer transition probabilities based on the cell’s velocity-extrapolated cell state and the cell states of its K nearest neighbors.

Parameters
  • mode (str) –

    How to compute transition probabilities. Valid options are:

    • ’deterministic’ - deterministic computation that doesn’t propagate uncertainty.

    • ’monte_carlo’ - Monte Carlo average of randomly sampled velocity vectors.

    • ’stochastic’ - second order approximation, only available when jax is installed.

    • ’sampling’ - sample 1 transition matrix from the velocity distribution.

  • backward_mode (str) –

    Only matters if initialized as backward =True. Valid options are:

    • ’transpose’ - compute transitions from neighboring cells j to cell i.

    • ’negate’ - negate the velocity vector.

  • softmax_scale (Optional[float]) – Scaling parameter for the softmax. If None, it will be estimated using 1 / median(correlations). The idea behind this is to scale the softmax to counteract everything tending to orthogonality in high dimensions.

  • scheme (Union[str, Callable]) –

    Similarity scheme between cells as described in [Li et al., 2021]. Can be one of the following:

    Alternatively, any function can be passed as long as it follows the signature of cellrank.tl.kernels.SimilaritySchemeABC.__call__().

  • n_samples (int) – Number of bootstrap samples when mode='monte_carlo'.

  • seed (Optional[int]) – Set the seed for random state when the method requires n_samples.

  • check_irreducibility (bool) – Optional check for irreducibility of the final transition matrix.

  • show_progress_bar – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend – Which backend to use for parallelization. See joblib.Parallel for valid options.

Returns

Makes available the following fields:

Return type

cellrank.tl.kernels.VelocityKernel

property logits: scipy.sparse.csr.csr_matrix

Array of shape (n_cells, n_cells) containing the logits.

Return type

csr_matrix

copy()[source]

Return a copy of self.

Return type

VelocityKernel

Cosine Similarity Scheme

class cellrank.tl.kernels.CosineScheme[source]

Cosine similarity scheme as defined in eq. (4.7) [Li et al., 2021].

\(v(s_i, s_j) = g(cos(\delta_{i, j}, v_i))\)

where \(v_i\) is the velocity vector of cell \(i\), \(\delta_{i, j}\) corresponds to the transcriptional displacement between cells \(i\) and \(j\) and \(g\) is a softmax function with some scaling parameter.

__call__(v, D, softmax_scale=1.0)

Compute transition probability of a cell to its nearest neighbors using RNA velocity.

Parameters
  • v (ndarray) – Array of shape (n_genes,) or (n_neighbors, n_genes) containing the velocity vector(s). The second case is used for the backward process.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The probability and logits arrays of shape (n_neighbors,).

Return type

numpy.ndarray, numpy.ndarray

hessian(v, D, softmax_scale=1.0)

Compute the Hessian.

Parameters
  • v (ndarray) – Array of shape (n_genes,) containing the velocity vector.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The full Hessian of shape (n_neighbors, n_genes, n_genes) or only its diagonal of shape (n_neighbors, n_genes).

Return type

numpy.ndarray

Correlation Scheme

class cellrank.tl.kernels.CorrelationScheme[source]

Pearson correlation scheme as defined in eq. (4.8) [Li et al., 2021].

\(v(s_i, s_j) = g(corr(\delta_{i, j}, v_i))\)

where \(v_i\) is the velocity vector of cell \(i\), \(\delta_{i, j}\) corresponds to the transcriptional displacement between cells \(i\) and \(j\) and \(g\) is a softmax function with some scaling parameter.

__call__(v, D, softmax_scale=1.0)

Compute transition probability of a cell to its nearest neighbors using RNA velocity.

Parameters
  • v (ndarray) – Array of shape (n_genes,) or (n_neighbors, n_genes) containing the velocity vector(s). The second case is used for the backward process.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The probability and logits arrays of shape (n_neighbors,).

Return type

numpy.ndarray, numpy.ndarray

hessian(v, D, softmax_scale=1.0)

Compute the Hessian.

Parameters
  • v (ndarray) – Array of shape (n_genes,) containing the velocity vector.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The full Hessian of shape (n_neighbors, n_genes, n_genes) or only its diagonal of shape (n_neighbors, n_genes).

Return type

numpy.ndarray

Dot Product Scheme

class cellrank.tl.kernels.DotProductScheme[source]

Dot product scheme as defined in eq. (4.9) [Li et al., 2021].

\(v(s_i, s_j) = g(\delta_{i, j}^T v_i)\)

where \(v_i\) is the velocity vector of cell \(i\), \(\delta_{i, j}\) corresponds to the transcriptional displacement between cells \(i\) and \(j\) and \(g\) is a softmax function with some scaling parameter.

__call__(v, D, softmax_scale=1.0)

Compute transition probability of a cell to its nearest neighbors using RNA velocity.

Parameters
  • v (ndarray) – Array of shape (n_genes,) or (n_neighbors, n_genes) containing the velocity vector(s). The second case is used for the backward process.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The probability and logits arrays of shape (n_neighbors,).

Return type

numpy.ndarray, numpy.ndarray

hessian(v, D, softmax_scale=1.0)

Compute the Hessian.

Parameters
  • v (ndarray) – Array of shape (n_genes,) containing the velocity vector.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The full Hessian of shape (n_neighbors, n_genes, n_genes) or only its diagonal of shape (n_neighbors, n_genes).

Return type

numpy.ndarray

Connectivity Kernel

class cellrank.tl.kernels.ConnectivityKernel(adata, backward=False, conn_key='connectivities', compute_cond_num=False, check_connectivity=False)[source]

Kernel which computes transition probabilities based on similarities among cells.

As a measure of similarity, we currently support:

The resulting transition matrix is symmetric and thus cannot be used to learn about the direction of the biological process. To include this direction, consider combining with a velocity-derived transition matrix via cellrank.tl.kernels.VelocityKernel.

Optionally, we apply a density correction as described in [Coifman et al., 2005], where we use the implementation of [Haghverdi et al., 2016].

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • conn_key (str) – Key in anndata.AnnData.obsp to obtain the connectivity matrix describing cell-cell similarity.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • check_connectivity (bool) – Check whether the underlying KNN graph is connected.

compute_transition_matrix(density_normalize=True)[source]

Compute transition matrix based on transcriptomic similarity.

Uses symmetric, weighted KNN graph to compute symmetric transition matrix. The connectivities are computed using scanpy.pp.neighbors(). Depending on the parameters used there, they can be UMAP connectivities or gaussian-kernel-based connectivities with adaptive kernel width.

Parameters

density_normalize (bool) – Whether or not to use the underlying KNN graph for density normalization.

Returns

Makes transition_matrix available.

Return type

cellrank.tl.kernels.ConnectivityKernel

copy()[source]

Return a copy of self.

Return type

ConnectivityKernel

Pseudotime Kernel

class cellrank.tl.kernels.PseudotimeKernel(adata, backward=False, time_key='dpt_pseudotime', compute_cond_num=False, check_connectivity=False, **kwargs)[source]

Kernel which computes directed transition probabilities based on a KNN graph and pseudotime.

The KNN graph contains information about the (undirected) connectivities among cells, reflecting their similarity. Pseudotime can be used to either remove edges that point against the direction of increasing pseudotime [Setty et al., 2019], or to downweight them [Stassen et al., 2021].

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • time_key (str) – Key in adata .obs where the pseudotime is stored.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • kwargs (Any) – Keyword arguments for cellrank.tl.kernels.Kernel.

compute_transition_matrix(threshold_scheme='hard', frac_to_keep=0.3, b=10.0, nu=0.5, check_irreducibility=False, n_jobs=None, backend='loky', show_progress_bar=True, **kwargs)[source]

Compute transition matrix based on KNN graph and pseudotemporal ordering.

Depending on the choice of the thresholding_scheme, this is based on ideas by either Palantir [Setty et al., 2019] or VIA [Stassen et al., 2021].

When using a ‘hard’ thresholding scheme, this based on ideas by Palantir [Setty et al., 2019] which removes some edges that point against the direction of increasing pseudotime. To avoid disconnecting the graph, it does not remove all edges that point against the direction of increasing pseudotime but keeps the ones that point to cells inside a close radius. This radius is chosen according to the local cell density.

When using a ‘soft’ thresholding scheme, this is based on ideas by VIA [Stassen et al., 2021] which downweights edges that points against the direction of increasing pseudotime. Essentially, the further “behind” a query cell is in pseudotime with respect to the current reference cell, the more penalized will be its graph-connectivity.

Parameters
  • frac_to_keep (float) – The frac_to_keep * n_neighbors closest neighbors (according to graph connectivities) are kept, no matter whether they lie in the pseudotemporal past or future. This is done to ensure that the graph remains connected. Only used when threshold_scheme=’hard’. frac_to_keep needs to fall within the interval [0, 1].

  • b (float) – The growth rate of generalized logistic function. Only used when threshold_scheme=’soft’.

  • nu (float) – Affects near which asymptote maximum growth occurs. Only used when threshold_scheme=’soft’.

  • check_irreducibility (bool) – Optional check for irreducibility of the final transition matrix.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

  • kwargs (Any) – Keyword arguments for threshold_scheme.

Returns

Makes transition_matrix available.

Return type

cellrank.tl.kernels.PseudotimeKernel

property pseudotime: numpy.array

Pseudotemporal ordering of cells.

Return type

array

copy()[source]

Return a copy of self.

Return type

PseudotimeKernel

Hard Threshold Scheme

class cellrank.tl.kernels.HardThresholdScheme[source]

Thresholding scheme inspired by Palantir [Setty et al., 2019].

Note that this won’t exactly reproduce the original Palantir results, for three reasons:

  • Palantir computes the KNN graph in a scaled space of diffusion components.

  • Palantir uses its own pseudotime to bias the KNN graph which is not implemented here.

  • Palantir uses a slightly different mechanism to ensure the graph remains connected when removing edges that point into the “pseudotime past”.

__call__(cell_pseudotime, neigh_pseudotime, neigh_conn, n_neighs, frac_to_keep=0.3)[source]

Convert the undirected graph of cell-cell similarities into a directed one by removing “past” edges.

This uses a pseudotemporal measure to remove graph-edges that point into the pseudotime-past. For each cell, it keeps the closest neighbors, even if they are in the pseudotime past, to make sure the graph remains connected.

Parameters
  • cell_pseudotime (float) – Pseudotime of the current cell.

  • neigh_pseudotime (ndarray) – Array of shape (n_neighbors,) containing pseudotimes of neighbors.

  • neigh_conn (ndarray) – Array of shape (n_neighbors,) containing connectivities of the current cell and its neighbors.

  • n_neighs (int) – Number of neighbors to keep.

  • frac_to_keep (float) – The frac_to_keep * n_neighbors closest neighbors (according to graph connectivities) are kept, no matter whether they lie in the pseudotemporal past or future. frac_to_keep needs to fall within the interval [0, 1].

Returns

Return type

Array of shape (n_neighbors,) containing the biased connectivities.

Soft Threshold Scheme

class cellrank.tl.kernels.SoftThresholdScheme[source]

Thresholding scheme inspired by [Stassen et al., 2021].

The idea is to downweight edges that points against the direction of increasing pseudotime. Essentially, the further “behind” a query cell is in pseudotime with respect to the current reference cell, the more penalized will be its graph-connectivity.

__call__(cell_pseudotime, neigh_pseudotime, neigh_conn, b=10.0, nu=0.5)[source]

Bias the connectivities by downweighting ones to past cells.

This function uses generalized logistic regression to weight the past connectivities.

Parameters
  • cell_pseudotime (float) – Pseudotime of the current cell.

  • neigh_pseudotime (ndarray) – Array of shape (n_neighbors,) containing pseudotimes of neighbors.

  • neigh_conn (ndarray) – Array of shape (n_neighbors,) containing connectivities of the current cell and its neighbors.

  • b (float) – The growth rate of generalized logistic function.

  • nu (float) – Affects near which asymptote maximum growth occurs.

Returns

Return type

Array of shape (n_neighbors,) containing the biased connectivities.

CytoTRACE Kernel

class cellrank.tl.kernels.CytoTRACEKernel(adata, backward=False, layer='Ms', aggregation='mean', use_raw=False, compute_cond_num=False, check_connectivity=False, **kwargs)[source]

Kernel which computes directed transition probabilities based on a KNN graph and the CytoTRACE score [Gulati et al., 2020].

The KNN graph contains information about the (undirected) connectivities among cells, reflecting their similarity. CytoTRACE can be used to estimate cellular plasticity and in turn, a pseudotemporal ordering of cells from more plastic to less plastic states. This kernel internally uses the cellrank.tl.kernels.PseudotimeKernel to direct the KNN graph on the basis of the CytoTRACE-derived pseudotime.

Optionally, we apply a density correction as described in [Coifman et al., 2005], where we use the implementation of [Haghverdi et al., 2016].

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • layer (str) – Key in anndata.AnnData.layers or ‘X’ for anndata.AnnData.X from where to get the expression.

  • aggregation (Literal[‘mean’, ‘median’, ‘hmean’, ‘gmean’]) –

    How to aggregate expression of the top-correlating genes. Valid options are:

    • ’mean’: arithmetic mean.

    • ’median’: median.

    • ’gmean’: geometric mean.

    • ’hmean’: harmonic mean.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • check_connectivity (bool) – Check whether the underlying KNN graph is connected.

  • kwargs (Any) – Keyword arguments for cellrank.tl.kernels.PseudotimeKernel.

Example

Workflow:

# import packages and load data
import scvelo as scv
import cellrank as cr
adata = cr.datasets.pancreas()

# standard pre-processing
sc.pp.filter_genes(adata, min_cells=10)
sc.pp.normalize_total(adata)
sc.pp.log1p(adata)
sc.pp.highly_variable_genes(adata)

# CytoTRACE by default uses imputed data - a simple way to compute KNN-imputed data is to use scVelo's moments
# function. However, note that this function expects `spliced` counts because it's designed for RNA velocity,
# so we're using a simple hack here:
if 'spliced' not in adata.layers or 'unspliced' not in adata.layers:
    adata.layers['spliced'] = adata.X
    adata.layers['unspliced'] = adata.X

# compute KNN-imputation using scVelo's moments function
scv.pp.moments(adata)

# import and initialize the CytoTRACE kernel, compute transition matrix - done!
from cellrank.tl.kernels import CytoTRACEKernel
ctk = CytoTRACEKernel(adata).compute_transition_matrix()
compute_cytotrace(layer='Ms', aggregation='mean', use_raw=False)[source]

Re-implementation of the CytoTRACE algorithm [Gulati et al., 2020] to estimate cellular plasticity.

Computes the number of genes expressed per cell and ranks genes according to their correlation with this measure. Next, it selects to top-correlating genes and aggregates their (imputed) expression to obtain the CytoTRACE score. A high score stands for high differentiation potential (naive, plastic cells) and a low score stands for low differentiation potential (mature, differentiation cells).

Parameters
  • layer (str) – Key in anndata.AnnData.layers or ‘X’ for anndata.AnnData.X from where to get the expression.

  • aggregation (Literal[‘mean’, ‘median’, ‘hmean’, ‘gmean’]) –

    How to aggregate expression of the top-correlating genes. Valid options are:

    • ’mean’: arithmetic mean.

    • ’median’: median.

    • ’gmean’: geometric mean.

    • ’hmean’: harmonic mean.

  • use_raw (bool) – Whether to use the anndata.AnnData.raw to compute the number of genes expressed per cell (#genes/cell) and the correlation of gene expression across cells with #genes/cell.

Return type

None

Returns

  • Nothing, just modifies anndata.AnnData.obs with the following keys –

    • ‘ct_score’: the normalized CytoTRACE score.

    • ’ct_pseudotime’: associated pseudotime, essentially 1 - CytoTRACE score.

    • ’ct_num_exp_genes’: the number of genes expressed per cell, basis of the CytoTRACE score.

  • It also modifies anndata.AnnData.var with the following keys –

    • ‘ct_gene_corr’: the correlation as specified above.

    • ’ct_correlates’: indication of the genes used to compute the CytoTRACE score, i.e. the ones that correlated best with ‘num_exp_genes’.

Notes

This will not exactly reproduce the results of the original CytoTRACE algorithm [Gulati et al., 2020] because we allow for any normalization and imputation techniques whereas CytoTRACE has built-in specific methods for that.

compute_transition_matrix(threshold_scheme='hard', frac_to_keep=0.3, b=10.0, nu=0.5, check_irreducibility=False, n_jobs=None, backend='loky', show_progress_bar=True, **kwargs)

Compute transition matrix based on KNN graph and pseudotemporal ordering.

Depending on the choice of the thresholding_scheme, this is based on ideas by either Palantir [Setty et al., 2019] or VIA [Stassen et al., 2021].

When using a ‘hard’ thresholding scheme, this based on ideas by Palantir [Setty et al., 2019] which removes some edges that point against the direction of increasing pseudotime. To avoid disconnecting the graph, it does not remove all edges that point against the direction of increasing pseudotime but keeps the ones that point to cells inside a close radius. This radius is chosen according to the local cell density.

When using a ‘soft’ thresholding scheme, this is based on ideas by VIA [Stassen et al., 2021] which downweights edges that points against the direction of increasing pseudotime. Essentially, the further “behind” a query cell is in pseudotime with respect to the current reference cell, the more penalized will be its graph-connectivity.

Parameters
  • frac_to_keep (float) – The frac_to_keep * n_neighbors closest neighbors (according to graph connectivities) are kept, no matter whether they lie in the pseudotemporal past or future. This is done to ensure that the graph remains connected. Only used when threshold_scheme=’hard’. frac_to_keep needs to fall within the interval [0, 1].

  • b (float) – The growth rate of generalized logistic function. Only used when threshold_scheme=’soft’.

  • nu (float) – Affects near which asymptote maximum growth occurs. Only used when threshold_scheme=’soft’.

  • check_irreducibility (bool) – Optional check for irreducibility of the final transition matrix.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

  • kwargs (Any) – Keyword arguments for threshold_scheme.

Returns

Makes transition_matrix available.

Return type

cellrank.tl.kernels.PseudotimeKernel

Precomputed Kernel

class cellrank.tl.kernels.PrecomputedKernel(transition_matrix=None, adata=None, backward=False, compute_cond_num=False, **kwargs)[source]

Kernel which contains a precomputed transition matrix.

Parameters
  • transition_matrix (Union[ndarray, spmatrix, KernelExpression, str, None]) – Row-normalized transition matrix or a key in adata .obsp or a cellrank.tl.kernels.KernelExpression with a precomputed transition matrix. If None, try to determine the key based on backward.

  • adata (anndata.AnnData) – Annotated data object. If None, a temporary placeholder object is created.

  • backward (bool) – Direction of the process.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • kwargs (Any) – Keyword arguments for cellrank.tl.kernels.Kernel.

copy()[source]

Return a copy of self.

Return type

PrecomputedKernel

compute_transition_matrix(*args, **kwargs)[source]

Return self.

Return type

PrecomputedKernel

Models

GAM

class cellrank.ul.models.GAM(adata, n_knots=6, spline_order=3, distribution='gamma', link='log', max_iter=2000, expectile=None, grid=None, spline_kwargs=mappingproxy({}), **kwargs)[source]

Fit Generalized Additive Models (GAMs) using pygam.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • n_knots (Optional[int]) – Number of knots.

  • spline_order (int) – Order of the splines, i.e. 3 for cubic splines.

  • distribution (str) – Name of the distribution. Available distributions can be found here.

  • link (str) – Name of the link function. Available link functions can be found here.

  • max_iter (int) – Maximum number of iterations for optimization.

  • expectile (Optional[float]) – Expectile for pygam.pygam.ExpectileGAM. This forces the distribution to be ‘normal’ and link function to ‘identity’. Must be in interval (0, 1).

  • grid (Union[str, Mapping, None]) – Whether to perform a grid search. Keys correspond to a parameter names and values to range to be searched. If ‘default’, use the default grid. If None, don’t perform a grid search.

  • spline_kwargs (Mapping) – Keyword arguments for pygam.s.

  • kwargs – Keyword arguments for pygam.pygam.GAM.

fit(x=None, y=None, w=None, **kwargs)[source]

Fit the model.

Parameters
  • x (Optional[ndarray]) – Independent variables, array of shape (n_samples, 1). If None, use x.

  • y (Optional[ndarray]) – Dependent variables, array of shape (n_samples, 1). If None, use y.

  • w (Optional[ndarray]) – Optional weights of x, array of shape (n_samples,). If None, use w.

  • kwargs – Keyword arguments for underlying model’s fitting function.

Returns

Fits the model and returns self.

Return type

cellrank.ul.models.GAM

predict(x_test=None, key_added='_x_test', **kwargs)[source]

Run the prediction.

Parameters
  • x_test (Optional[ndarray]) – Array of shape (n_samples,) used for prediction. If None, use x_test.

  • key_added (Optional[str]) – Attribute name where to save the x_test for later use. If None, don’t save it.

  • kwargs – Keyword arguments for underlying model’s prediction method.

Returns

Updates and returns the following:

  • y_test - Prediction values of shape (n_samples,) for x_test.

Return type

numpy.ndarray

property adata: cellrank.ul.models._base_model.AnnData

Annotated data object.

Returns

adata – Annotated data object.

Return type

anndata.AnnData

property conf_int: numpy.ndarray

Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

ndarray

confidence_interval(x_test=None, **kwargs)[source]

Calculate the confidence interval.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

numpy.ndarray

default_confidence_interval(x_test=None, **kwargs)

Calculate the confidence interval, if the underlying model has no method for it.

This formula is taken from [DeSalvo, 1970], eq. 5.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

  • x_hat - Filtered independent variables used when calculating default confidence interval, usually same as x.

  • y_hat - Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

numpy.ndarray

property model: Any

The underlying model.

Return type

Any

plot(figsize=(8, 5), same_plot=False, hide_cells=False, perc=None, abs_prob_cmap=<matplotlib.colors.ListedColormap object>, cell_color=None, lineage_color='black', alpha=0.8, lineage_alpha=0.2, title=None, size=15, lw=2, cbar=True, margins=0.015, xlabel='pseudotime', ylabel='expression', conf_int=True, lineage_probability=False, lineage_probability_conf_int=False, lineage_probability_color=None, obs_legend_loc='best', dpi=None, fig=None, ax=None, return_fig=False, save=None, **kwargs)

Plot the smoothed gene expression.

Parameters
  • figsize (Tuple[float, float]) – Size of the figure.

  • same_plot (bool) – Whether to plot all trends in the same plot.

  • hide_cells (bool) – Whether to hide the cells.

  • perc (Optional[Tuple[float, float]]) – Percentile by which to clip the absorption probabilities.

  • abs_prob_cmap (ListedColormap) – Colormap to use when coloring in the absorption probabilities.

  • cell_color (Optional[str]) – Key in anndata.AnnData.obs or anndata.AnnData.var_names used for coloring the cells.

  • lineage_color (str) – Color for the lineage.

  • alpha (float) – Alpha channel for cells.

  • lineage_alpha (float) – Alpha channel for lineage confidence intervals.

  • title (Optional[str]) – Title of the plot.

  • size (int) – Size of the points.

  • lw (float) – Line width for the smoothed values.

  • cbar (bool) – Whether to show colorbar.

  • margins (float) – Margins around the plot.

  • xlabel (str) – Label on the x-axis.

  • ylabel (str) – Label on the y-axis.

  • conf_int (bool) – Whether to show the confidence interval.

  • lineage_probability (bool) – Whether to show smoothed lineage probability as a dashed line. Note that this will require 1 additional model fit.

  • lineage_probability_conf_int (Union[bool, float]) – Whether to compute and show smoothed lineage probability confidence interval. If self is cellrank.ul.models.GAMR, it can also specify the confidence level, the default is 0.95. Only used when show_lineage_probability=True.

  • lineage_probability_color (Optional[str]) – Color to use when plotting the smoothed lineage_probability. If None, it’s the same as lineage_color. Only used when show_lineage_probability=True.

  • obs_legend_loc (Optional[str]) – Location of the legend when cell_color corresponds to a categorical variable.

  • dpi (Optional[int]) – Dots per inch.

  • fig (Optional[Figure]) – Figure to use, if None, create a new one.

  • ax (matplotlib.axes.Axes) – Ax to use, if None, create a new one.

  • return_fig (bool) – If True, return the figure object.

  • save (Optional[str]) – Filename where to save the plot. If None, just shows the plots.

  • kwargs – Keyword arguments for matplotlib.axes.Axes.legend(), e.g. to disable the legend, specify loc=None. Only available when show_lineage_probability=True.

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

prepare(gene, lineage, backward=False, time_range=None, data_key='X', time_key='latent_time', use_raw=False, threshold=None, weight_threshold=(0.01, 0.01), filter_cells=None, n_test_points=200)

Prepare the model to be ready for fitting.

Parameters
  • gene (str) – Gene in adata .var_names or in adata .raw.var_names.

  • lineage (Optional[str]) – Name of a lineage in adata .obsm['{lineage_key}']. If None, all weights will be set to 1.

  • backward (bool) – Direction of the process.

  • time_range (Union[float, Tuple[float, float], None]) –

    Specify start and end times:

    • If a tuple, it specifies the minimum and maximum pseudotime. Both values can be None, in which case the minimum is the earliest pseudotime and the maximum is automatically determined.

    • If a float, it specifies the maximum pseudotime.

  • data_key (str) – Key in adata .layers or ‘X’ for adata .X. If use_raw=True, it’s always set to ‘X’.

  • time_key (str) – Key in adata .obs where the pseudotime is stored.

  • use_raw (bool) – Whether to access adata .raw or not.

  • threshold (Optional[float]) – Consider only cells with weights > threshold when estimating the test endpoint. If None, use the median of the weights.

  • weight_threshold (Union[float, Tuple[float, float]]) – Set all weights below weight_threshold to weight_threshold if a float, or to the second value, if a tuple.

  • filter_cells (Optional[float]) – Filter out all cells with expression values lower than this threshold.

  • n_test_points (int) – Number of test points. If None, use the original points based on threshold.

Returns

Nothing, but updates the following fields:

  • x - Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

  • y - Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

  • w - Filtered weights of shape (n_filtered_cells,) used for fitting.

  • x_all - Unfiltered independent variables of shape (n_cells, 1).

  • y_all - Unfiltered dependent variables of shape (n_cells, 1).

  • w_all - Unfiltered weights of shape (n_cells,).

  • x_test - Independent variables of shape (n_samples, 1) used for prediction.

  • prepared - Whether the model is prepared for fitting.

Return type

None

property prepared

Whether the model is prepared for fitting.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property w: numpy.ndarray

Filtered weights of shape (n_filtered_cells,) used for fitting.

Return type

ndarray

property w_all: numpy.ndarray

Unfiltered weights of shape (n_cells,).

Return type

ndarray

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

property x: numpy.ndarray

Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property x_all: numpy.ndarray

Unfiltered independent variables of shape (n_cells, 1).

Return type

ndarray

property x_hat: numpy.ndarray

Filtered independent variables used when calculating default confidence interval, usually same as x.

Return type

ndarray

property x_test: numpy.ndarray

Independent variables of shape (n_samples, 1) used for prediction.

Return type

ndarray

property y: numpy.ndarray

Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property y_all: numpy.ndarray

Unfiltered dependent variables of shape (n_cells, 1).

Return type

ndarray

property y_hat: numpy.ndarray

Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

ndarray

property y_test: numpy.ndarray

Prediction values of shape (n_samples,) for x_test.

Return type

ndarray

copy()[source]

Return a copy of self.

Return type

BaseModel

SKLearnModel

class cellrank.ul.models.SKLearnModel(adata, model, weight_name=None, ignore_raise=False)[source]

Wrapper around sklearn.base.BaseEstimator.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • model (BaseEstimator) – Instance of the underlying sklearn estimator, such as sklearn.svm.SVR.

  • weight_name (Optional[str]) – Name of the weight argument for model .fit. If None, to determine it automatically. If and empty string, no weights will be used.

  • ignore_raise (bool) – Do not raise an exception if weight argument is not found in the fitting function of model. This is useful in case when weight is passed in **kwargs and cannot be determined from signature.

fit(x=None, y=None, w=None, **kwargs)[source]

Fit the model.

Parameters
  • x (Optional[ndarray]) – Independent variables, array of shape (n_samples, 1). If None, use x.

  • y (Optional[ndarray]) – Dependent variables, array of shape (n_samples, 1). If None, use y.

  • w (Optional[ndarray]) – Optional weights of x, array of shape (n_samples,). If None, use w.

  • kwargs – Keyword arguments for underlying model’s fitting function.

Returns

Fits the model and returns self.

Return type

cellrank.ul.models.SKLearnModel

predict(x_test=None, key_added='_x_test', **kwargs)[source]

Run the prediction.

Parameters
  • x_test (Optional[ndarray]) – Array of shape (n_samples,) used for prediction. If None, use x_test.

  • key_added (str) – Attribute name where to save the x_test for later use. If None, don’t save it.

  • kwargs – Keyword arguments for underlying model’s prediction method.

Returns

Updates and returns the following:

  • y_test - Prediction values of shape (n_samples,) for x_test.

Return type

numpy.ndarray

confidence_interval(x_test=None, **kwargs)[source]

Calculate the confidence interval.

Use default_confidence_interval() function if underlying model has not method for confidence interval calculation.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

numpy.ndarray

property model: sklearn.base.BaseEstimator

The underlying sklearn.base.BaseEstimator.

Return type

BaseEstimator

copy()[source]

Return a copy of self.

Return type

SKLearnModel

property adata: cellrank.ul.models._base_model.AnnData

Annotated data object.

Returns

adata – Annotated data object.

Return type

anndata.AnnData

property conf_int: numpy.ndarray

Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

ndarray

default_confidence_interval(x_test=None, **kwargs)

Calculate the confidence interval, if the underlying model has no method for it.

This formula is taken from [DeSalvo, 1970], eq. 5.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

  • x_hat - Filtered independent variables used when calculating default confidence interval, usually same as x.

  • y_hat - Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

numpy.ndarray

plot(figsize=(8, 5), same_plot=False, hide_cells=False, perc=None, abs_prob_cmap=<matplotlib.colors.ListedColormap object>, cell_color=None, lineage_color='black', alpha=0.8, lineage_alpha=0.2, title=None, size=15, lw=2, cbar=True, margins=0.015, xlabel='pseudotime', ylabel='expression', conf_int=True, lineage_probability=False, lineage_probability_conf_int=False, lineage_probability_color=None, obs_legend_loc='best', dpi=None, fig=None, ax=None, return_fig=False, save=None, **kwargs)

Plot the smoothed gene expression.

Parameters
  • figsize (Tuple[float, float]) – Size of the figure.

  • same_plot (bool) – Whether to plot all trends in the same plot.

  • hide_cells (bool) – Whether to hide the cells.

  • perc (Optional[Tuple[float, float]]) – Percentile by which to clip the absorption probabilities.

  • abs_prob_cmap (ListedColormap) – Colormap to use when coloring in the absorption probabilities.

  • cell_color (Optional[str]) – Key in anndata.AnnData.obs or anndata.AnnData.var_names used for coloring the cells.

  • lineage_color (str) – Color for the lineage.

  • alpha (float) – Alpha channel for cells.

  • lineage_alpha (float) – Alpha channel for lineage confidence intervals.

  • title (Optional[str]) – Title of the plot.

  • size (int) – Size of the points.

  • lw (float) – Line width for the smoothed values.

  • cbar (bool) – Whether to show colorbar.

  • margins (float) – Margins around the plot.

  • xlabel (str) – Label on the x-axis.

  • ylabel (str) – Label on the y-axis.

  • conf_int (bool) – Whether to show the confidence interval.

  • lineage_probability (bool) – Whether to show smoothed lineage probability as a dashed line. Note that this will require 1 additional model fit.

  • lineage_probability_conf_int (Union[bool, float]) – Whether to compute and show smoothed lineage probability confidence interval. If self is cellrank.ul.models.GAMR, it can also specify the confidence level, the default is 0.95. Only used when show_lineage_probability=True.

  • lineage_probability_color (Optional[str]) – Color to use when plotting the smoothed lineage_probability. If None, it’s the same as lineage_color. Only used when show_lineage_probability=True.

  • obs_legend_loc (Optional[str]) – Location of the legend when cell_color corresponds to a categorical variable.

  • dpi (Optional[int]) – Dots per inch.

  • fig (Optional[Figure]) – Figure to use, if None, create a new one.

  • ax (matplotlib.axes.Axes) – Ax to use, if None, create a new one.

  • return_fig (bool) – If True, return the figure object.

  • save (Optional[str]) – Filename where to save the plot. If None, just shows the plots.

  • kwargs – Keyword arguments for matplotlib.axes.Axes.legend(), e.g. to disable the legend, specify loc=None. Only available when show_lineage_probability=True.

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

prepare(gene, lineage, backward=False, time_range=None, data_key='X', time_key='latent_time', use_raw=False, threshold=None, weight_threshold=(0.01, 0.01), filter_cells=None, n_test_points=200)

Prepare the model to be ready for fitting.

Parameters
  • gene (str) – Gene in adata .var_names or in adata .raw.var_names.

  • lineage (Optional[str]) – Name of a lineage in adata .obsm['{lineage_key}']. If None, all weights will be set to 1.

  • backward (bool) – Direction of the process.

  • time_range (Union[float, Tuple[float, float], None]) –

    Specify start and end times:

    • If a tuple, it specifies the minimum and maximum pseudotime. Both values can be None, in which case the minimum is the earliest pseudotime and the maximum is automatically determined.

    • If a float, it specifies the maximum pseudotime.

  • data_key (str) – Key in adata .layers or ‘X’ for adata .X. If use_raw=True, it’s always set to ‘X’.

  • time_key (str) – Key in adata .obs where the pseudotime is stored.

  • use_raw (bool) – Whether to access adata .raw or not.

  • threshold (Optional[float]) – Consider only cells with weights > threshold when estimating the test endpoint. If None, use the median of the weights.

  • weight_threshold (Union[float, Tuple[float, float]]) – Set all weights below weight_threshold to weight_threshold if a float, or to the second value, if a tuple.

  • filter_cells (Optional[float]) – Filter out all cells with expression values lower than this threshold.

  • n_test_points (int) – Number of test points. If None, use the original points based on threshold.

Returns

Nothing, but updates the following fields:

  • x - Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

  • y - Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

  • w - Filtered weights of shape (n_filtered_cells,) used for fitting.

  • x_all - Unfiltered independent variables of shape (n_cells, 1).

  • y_all - Unfiltered dependent variables of shape (n_cells, 1).

  • w_all - Unfiltered weights of shape (n_cells,).

  • x_test - Independent variables of shape (n_samples, 1) used for prediction.

  • prepared - Whether the model is prepared for fitting.

Return type

None

property prepared

Whether the model is prepared for fitting.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property w: numpy.ndarray

Filtered weights of shape (n_filtered_cells,) used for fitting.

Return type

ndarray

property w_all: numpy.ndarray

Unfiltered weights of shape (n_cells,).

Return type

ndarray

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

property x: numpy.ndarray

Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property x_all: numpy.ndarray

Unfiltered independent variables of shape (n_cells, 1).

Return type

ndarray

property x_hat: numpy.ndarray

Filtered independent variables used when calculating default confidence interval, usually same as x.

Return type

ndarray

property x_test: numpy.ndarray

Independent variables of shape (n_samples, 1) used for prediction.

Return type

ndarray

property y: numpy.ndarray

Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property y_all: numpy.ndarray

Unfiltered dependent variables of shape (n_cells, 1).

Return type

ndarray

property y_hat: numpy.ndarray

Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

ndarray

property y_test: numpy.ndarray

Prediction values of shape (n_samples,) for x_test.

Return type

ndarray

GAMR

class cellrank.ul.models.GAMR(adata, n_knots=5, distribution='gaussian', basis='cr', knotlocs='auto', offset='default', smoothing_penalty=1.0, **kwargs)[source]

Wrapper around R’s mgcv package for fitting Generalized Additive Models (GAMs).

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • n_knots (int) – Number of knots.

  • distribution (str) – Distribution family in rpy2.robjects.r, such as ‘gaussian’ or ‘nb’ for negative binomial. If ‘nb’, raw count data in adata .raw is always used.

  • basis (str) – Basis for the smoothing term. See here for valid options.

  • knotlocs (str) –

    Position of the knots. Can be one of the following:

    • ’auto’ - let mgcv handle the knot positions.

    • ’density’ - position the knots based on the density of the pseudotime.

  • offset (Union[str, ndarray, None]) – Offset term for the GAM. Only available when distribution='nb'. If ‘default’, it is calculated according to [Robinson and Oshlack, 2010]. The values are saved in adata .obs['cellrank_offset']. If None, no offset is used.

  • smoothing_penalty (float) – Penalty for the smoothing term. The larger the value, the smoother the fitted curve.

  • kwargs – Keyword arguments for gam.control. See here for reference.

prepare(*args, **kwargs)[source]

Prepare the model to be ready for fitting. This also removes the zero and negative weights and prepares the design matrix.

Parameters
  • gene – Gene in adata .var_names or in adata .raw.var_names.

  • lineage – Name of a lineage in adata .obsm['{lineage_key}']. If None, all weights will be set to 1.

  • backward – Direction of the process.

  • time_range

    Specify start and end times:

    • If a tuple, it specifies the minimum and maximum pseudotime. Both values can be None, in which case the minimum is the earliest pseudotime and the maximum is automatically determined.

    • If a float, it specifies the maximum pseudotime.

  • data_key – Key in adata .layers or ‘X’ for adata .X. If use_raw=True, it’s always set to ‘X’.

  • time_key – Key in adata .obs where the pseudotime is stored.

  • use_raw – Whether to access adata .raw or not.

  • threshold – Consider only cells with weights > threshold when estimating the test endpoint. If None, use the median of the weights.

  • weight_threshold – Set all weights below weight_threshold to weight_threshold if a float, or to the second value, if a tuple.

  • filter_cells – Filter out all cells with expression values lower than this threshold.

  • n_test_points – Number of test points. If None, use the original points based on threshold.

Returns

Nothing, but updates the following fields:

  • x - Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

  • y - Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

  • w - Filtered weights of shape (n_filtered_cells,) used for fitting.

  • x_all - Unfiltered independent variables of shape (n_cells, 1).

  • y_all - Unfiltered dependent variables of shape (n_cells, 1).

  • w_all - Unfiltered weights of shape (n_cells,).

  • x_test - Independent variables of shape (n_samples, 1) used for prediction.

  • prepared - Whether the model is prepared for fitting.

Return type

None

fit(x=None, y=None, w=None, **kwargs)[source]

Fit the model.

Parameters
  • x (Optional[ndarray]) – Independent variables, array of shape (n_samples, 1). If None, use x.

  • y (Optional[ndarray]) – Dependent variables, array of shape (n_samples, 1). If None, use y.

  • w (Optional[ndarray]) – Optional weights of x, array of shape (n_samples,). If None, use w.

  • kwargs – Keyword arguments for underlying model’s fitting function.

Returns

Fits the model and returns self. Updates the following fields by filtering out 0 weights w:

  • x - Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

  • y - Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

  • w - Filtered weights of shape (n_filtered_cells,) used for fitting.

Return type

cellrank.ul.models.GAMR

predict(x_test=None, key_added='_x_test', level=None, **kwargs)[source]

Run the prediction. This method can also compute the confidence interval.

Parameters
  • x_test (Optional[ndarray]) – Array of shape (n_samples,) used for prediction. If None, use x_test.

  • key_added (str) – Attribute name where to save the x_test for later use. If None, don’t save it.

  • kwargs – Keyword arguments for underlying model’s prediction method.

  • level (Optional[float]) – Confidence level for confidence interval calculation. If None, don’t compute the confidence interval. Must be in the interval [0, 1].

Returns

Updates and returns the following:

  • y_test - Prediction values of shape (n_samples,) for x_test.

Return type

numpy.ndarray

confidence_interval(x_test=None, level=0.95, **kwargs)[source]

Calculate the confidence interval. Internally, this method calls cellrank.ul.models.GAMR.predict() to extract the confidence interval, if needed.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

numpy.ndarray

copy()[source]

Return a copy of self.

Return type

GAMR

property adata: cellrank.ul.models._base_model.AnnData

Annotated data object.

Returns

adata – Annotated data object.

Return type

anndata.AnnData

property conf_int: numpy.ndarray

Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

ndarray

default_confidence_interval(x_test=None, **kwargs)

Calculate the confidence interval, if the underlying model has no method for it.

This formula is taken from [DeSalvo, 1970], eq. 5.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

  • x_hat - Filtered independent variables used when calculating default confidence interval, usually same as x.

  • y_hat - Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

numpy.ndarray

property model: Any

The underlying model.

Return type

Any

plot(figsize=(8, 5), same_plot=False, hide_cells=False, perc=None, abs_prob_cmap=<matplotlib.colors.ListedColormap object>, cell_color=None, lineage_color='black', alpha=0.8, lineage_alpha=0.2, title=None, size=15, lw=2, cbar=True, margins=0.015, xlabel='pseudotime', ylabel='expression', conf_int=True, lineage_probability=False, lineage_probability_conf_int=False, lineage_probability_color=None, obs_legend_loc='best', dpi=None, fig=None, ax=None, return_fig=False, save=None, **kwargs)

Plot the smoothed gene expression.

Parameters
  • figsize (Tuple[float, float]) – Size of the figure.

  • same_plot (bool) – Whether to plot all trends in the same plot.

  • hide_cells (bool) – Whether to hide the cells.

  • perc (Optional[Tuple[float, float]]) – Percentile by which to clip the absorption probabilities.

  • abs_prob_cmap (ListedColormap) – Colormap to use when coloring in the absorption probabilities.

  • cell_color (Optional[str]) – Key in anndata.AnnData.obs or anndata.AnnData.var_names used for coloring the cells.

  • lineage_color (str) – Color for the lineage.

  • alpha (float) – Alpha channel for cells.

  • lineage_alpha (float) – Alpha channel for lineage confidence intervals.

  • title (Optional[str]) – Title of the plot.

  • size (int) – Size of the points.

  • lw (float) – Line width for the smoothed values.

  • cbar (bool) – Whether to show colorbar.

  • margins (float) – Margins around the plot.

  • xlabel (str) – Label on the x-axis.

  • ylabel (str) – Label on the y-axis.

  • conf_int (bool) – Whether to show the confidence interval.

  • lineage_probability (bool) – Whether to show smoothed lineage probability as a dashed line. Note that this will require 1 additional model fit.

  • lineage_probability_conf_int (Union[bool, float]) – Whether to compute and show smoothed lineage probability confidence interval. If self is cellrank.ul.models.GAMR, it can also specify the confidence level, the default is 0.95. Only used when show_lineage_probability=True.

  • lineage_probability_color (Optional[str]) – Color to use when plotting the smoothed lineage_probability. If None, it’s the same as lineage_color. Only used when show_lineage_probability=True.

  • obs_legend_loc (Optional[str]) – Location of the legend when cell_color corresponds to a categorical variable.

  • dpi (Optional[int]) – Dots per inch.

  • fig (Optional[Figure]) – Figure to use, if None, create a new one.

  • ax (matplotlib.axes.Axes) – Ax to use, if None, create a new one.

  • return_fig (bool) – If True, return the figure object.

  • save (Optional[str]) – Filename where to save the plot. If None, just shows the plots.

  • kwargs – Keyword arguments for matplotlib.axes.Axes.legend(), e.g. to disable the legend, specify loc=None. Only available when show_lineage_probability=True.

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

property prepared

Whether the model is prepared for fitting.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property w: numpy.ndarray

Filtered weights of shape (n_filtered_cells,) used for fitting.

Return type

ndarray

property w_all: numpy.ndarray

Unfiltered weights of shape (n_cells,).

Return type

ndarray

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

property x: numpy.ndarray

Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property x_all: numpy.ndarray

Unfiltered independent variables of shape (n_cells, 1).

Return type

ndarray

property x_hat: numpy.ndarray

Filtered independent variables used when calculating default confidence interval, usually same as x.

Return type

ndarray

property x_test: numpy.ndarray

Independent variables of shape (n_samples, 1) used for prediction.

Return type

ndarray

property y: numpy.ndarray

Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property y_all: numpy.ndarray

Unfiltered dependent variables of shape (n_cells, 1).

Return type

ndarray

property y_hat: numpy.ndarray

Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

ndarray

property y_test: numpy.ndarray

Prediction values of shape (n_samples,) for x_test.

Return type

ndarray

Base Classes

BaseEstimator

class cellrank.tl.estimators.BaseEstimator(obj, inplace=True, read_from_adata=False, obsp_key=None, g2m_key='G2M_score', s_key='S_score', write_to_adata=True, key=None)[source]

Base class for all estimators.

Parameters
  • obj (Union[KernelExpression, ~AnnData, spmatrix, ndarray]) – Either a cellrank.tl.kernels.Kernel object, an anndata.AnnData object which stores the transition matrix in .obsp attribute or numpy or scipy array.

  • inplace (bool) – Whether to modify adata object inplace or make a copy.

  • read_from_adata (bool) – Whether to read available attributes in adata, if present.

  • obsp_key (Optional[str]) – Key in obj.obsp when obj is an anndata.AnnData object.

  • g2m_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • s_key (Optional[str]) – Key in adata .obs. Can be used to detect cell-cycle driven start- or endpoints.

  • write_to_adata (bool) – Whether to write the transition matrix to adata .obsp and the parameters to adata .uns.

  • key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’. Only used when write_to_adata=True.

set_terminal_states(labels, cluster_key=None, en_cutoff=None, p_thresh=None, add_to_existing=False, **kwargs)[source]

Manually define terminal states.

Parameters
  • labels (Union[Series, Dict[str, Sequence[Any]]]) –

    Defines the terminal states. Valid options are:

    • categorical pandas.Series where each category corresponds to one terminal state. NaN entries denote cells that do not belong to any terminal state, i.e. these are either initial or transient cells.

    • dict where keys are terminal states and values are lists of cell barcodes corresponding to annotations in adata .obs_names. If only 1 key is provided, values should correspond to terminal state clusters if a categorical pandas.Series can be found in adata .obs.

  • cluster_key (Optional[str]) – Key from adata.obs where categorical cluster labels are stored. These are used to associate names and colors with each terminal state. Each terminal state will be given the name and color corresponding to the cluster it mostly overlaps with.

  • en_cutoff (Optional[float]) – If cluster_key is given, this parameter determines when an approximate recurrent class will be labeled as ‘Unknown’, based on the entropy of the distribution of cells over transcriptomic clusters.

  • p_thresh (Optional[float]) – If cell cycle scores were provided, a Wilcoxon rank-sum test is conducted to identify cell-cycle states. If the test returns a positive statistic and a p-value smaller than p_thresh, a warning will be issued.

  • add_to_existing (bool) – Whether the new terminal states should be added to pre-existing ones. Cells already assigned to a terminal state will be re-assigned to the new terminal state if there’s a conflict between old and new annotations. This throws an error if no previous annotations corresponding to terminal states have been found.

Returns

Nothing, but updates the following fields:

  • terminal_states_probabilities

  • terminal_states

Return type

None

rename_terminal_states(new_names, update_adata=True)[source]

Rename the names of terminal_states.

Parameters
  • new_names (Mapping[str, str]) – Mapping where keys are the old names and the values are the new names. New names must be unique.

  • update_adata (bool) – Whether to update underlying adata object as well or not.

Returns

Nothing, just updates the names of terminal_states.

Return type

None

compute_absorption_probabilities(keys=None, check_irreducibility=False, solver='gmres', use_petsc=True, time_to_absorption=None, n_jobs=None, backend='loky', show_progress_bar=True, tol=1e-06, preconditioner=None)[source]

Compute absorption probabilities of a Markov chain.

For each cell, this computes the probability of it reaching any of the approximate recurrent classes defined by terminal_states.

Parameters
  • keys (Optional[Sequence[str]]) – Keys defining the recurrent classes.

  • check_irreducibility (bool) – Check whether the transition matrix is irreducible.

  • solver (str) –

    Solver to use for the linear problem. Options are ‘direct’, ‘gmres’, ‘lgmres’, ‘bicgstab’ or ‘gcrotmk’ when use_petsc=False or one of petsc4py.PETSc.KPS.Type otherwise.

    Information on the scipy iterative solvers can be found in scipy.sparse.linalg() or for petsc4py solver here.

  • use_petsc (bool) – Whether to use solvers from petsc4py or scipy. Recommended for large problems. If no installation is found, defaults to scipy.sparse.linalg.gmres().

  • time_to_absorption (Union[str, Sequence[Union[str, Sequence[str]]], Dict[Union[str, Sequence[str]], str], None]) –

    Whether to compute mean time to absorption and its variance to specific absorbing states.

    If a dict, can be specified as {'Alpha': 'var', ...} to also compute variance. In case when states are a tuple, time to absorption will be computed to the subset of these states, such as [('Alpha', 'Beta'), ...] or {('Alpha', 'Beta'): 'mean', ...}. Can be specified as 'all' to compute it to any absorbing state in keys, which is more efficient than listing all absorbing states.

    It might be beneficial to disable the progress bar as show_progress_bar=False, because many linear systems are being solved.

  • n_jobs (Optional[int]) – Number of parallel jobs to use when using an iterative solver. When use_petsc=True or for quickly-solvable problems, we recommend higher number (>=8) of jobs in order to fully saturate the cores.

  • backend (str) – Which backend to use for multiprocessing. See joblib.Parallel for valid options.

  • show_progress_bar (bool) – Whether to show progress bar when the solver isn’t a direct one.

  • tol (float) – Convergence tolerance for the iterative solver. The default is fine for most cases, only consider decreasing this for severely ill-conditioned matrices.

  • preconditioner (Optional[str]) – Preconditioner to use, only available when use_petsc=True. For available values, see here or the values of petsc4py.PETSc.PC.Type. We recommended ‘ilu’ preconditioner for badly conditioned problems.

Returns

Nothing, but updates the following fields:

  • absorption_probabilities - probabilities of being absorbed into the terminal states.

  • lineage_absorption_times - mean times until absorption to subset absorbing states and optionally their variances saved as '{lineage} mean' and '{lineage} var', respectively, for each subset of absorbing states specified in time_to_absorption.

Return type

None

compute_lineage_priming(method='kl_divergence', early_cells=None)[source]

Compute the degree of lineage priming.

This method computes how naive vs. committed each individual cell is. It returns a score where 0 stands for naive and 1 stands for committed.

Parameters
  • method (Literal[‘kl_divergence’, ‘entropy’]) –

    The method used to compute the degree of lineage priming. Valid options are:

    • ’kl_divergence’: as in [Velten et al., 2017], computes KL-divergence between the fate probabilities of a cell and the average fate probabilities. Computation of average fate probabilities can be restricted to a set of user-defined early_cells.

    • ’entropy’: as in [Setty et al., 2019], computes entropy over a cell’s fate probabilities.

  • early_cells (Union[Mapping[str, Sequence[str]], Sequence[str], None]) – Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'. If a dict, the key species a cluster key in anndata.AnnData.obs and the values specify cluster labels containing early cells.

Returns

Return type

The priming degree.

compute_lineage_drivers(lineages=None, method='fischer', cluster_key=None, clusters=None, layer='X', use_raw=False, confidence_level=0.95, n_perms=1000, seed=None, return_drivers=True, **kwargs)[source]

Compute driver genes per lineage.

Correlates gene expression with lineage probabilities, for a given lineage and set of clusters. Often, it makes sense to restrict this to a set of clusters which are relevant for the specified lineages.

Parameters
  • lineages (Union[str, Sequence, None]) – Either a set of lineage names from absorption_probabilities .names or None, in which case all lineages are considered.

  • method (str) –

    Mode to use when calculating p-values and confidence intervals. Valid options are:

    • ’fischer’ - use Fischer transformation [Fisher, 1921].

    • ’perm_test’ - use permutation test.

  • cluster_key (Optional[str]) – Key from adata .obs to obtain cluster annotations. These are considered for clusters.

  • clusters (Union[str, Sequence, None]) – Restrict the correlations to these clusters.

  • layer (str) – Key from adata .layers.

  • use_raw (bool) – Whether or not to use adata .raw to correlate gene expression. If using a layer other than .X, this must be set to False.

  • confidence_level (float) – Confidence level for the confidence interval calculation. Must be in [0, 1].

  • n_perms (int) – Number of permutations to use when method='perm_test'.

  • seed (Optional[int]) – Random seed when method='perm_test'.

  • return_drivers (bool) – Whether to return the drivers. This also contains the lower and upper confidence_level confidence interval bounds.

  • show_progress_bar – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend – Which backend to use for parallelization. See joblib.Parallel for valid options.

Return type

Optional[DataFrame]

Returns

  • Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, 1 for each lineage –

    • {lineage} corr - correlation between the gene expression and absorption probabilities.

    • {lineage} pval - calculated p-values for double-sided test.

    • {lineage} qval - corrected p-values using Benjamini-Hochberg method at level 0.05.

    • {lineage} ci low - lower bound of the confidence_level correlation confidence interval.

    • {lineage} ci high - upper bound of the confidence_level correlation confidence interval.

  • Only if return_drivers=True.

  • Otherwise, updates adata .var or adata .raw.var, depending use_raw with –

    • '{direction} {lineage} corr' - the potential lineage drivers.

    • '{direction} {lineage} qval' - the corrected p-values.

  • Also updates the following fields

    • lineage_drivers - same as the returned values.

plot_lineage_drivers(lineage, n_genes=8, ncols=None, use_raw=False, title_fmt='{gene} qval={qval:.4e}', figsize=None, dpi=None, save=None, **kwargs)[source]

Plot lineage drivers discovered by compute_lineage_drivers().

Parameters
  • lineage (str) – Lineage for which to plot the driver genes.

  • n_genes (int) – Top most correlated genes to plot.

  • ncols (Optional[int]) – Number of columns.

  • use_raw (bool) – Whether to look in adata .raw.var or adata .var.

  • title_fmt (str) – Title format. Possible keywords include {gene}, {qval}, {corr} for gene name, q-value and correlation, respectively.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs – Keyword arguments for scvelo.pl.scatter().

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

plot_lineage_drivers_correlation(lineage_x, lineage_y, color=None, gene_sets=None, gene_sets_colors=None, use_raw=False, cmap='RdYlBu_r', fontsize=12, adjust_text=False, legend_loc='best', figsize=(4, 4), dpi=None, save=None, show=True, **kwargs)[source]

Show scatter plot of gene-correlations between two lineages.

Optionally, you can pass a dict of gene names that will be annotated in the plot.

Parameters
  • lineage_x (str) – Name of the lineage on the x-axis.

  • lineage_y (str) – Name of the lineage on the y-axis.

  • color (Optional[str]) – Key in adata .var.

  • gene_sets (Optional[Dict[str, Iterable]]) – Gene sets annotations of the form {‘gene_set_name’: [‘gene_1’, ‘gene_2’], …}.

  • gene_sets_colors (Optional[Iterable]) – List of colors where each entry corresponds to a gene set from genes_sets. If None and keys in gene_sets correspond to lineage names, use the lineage colors. Otherwise, use default colors.

  • use_raw (bool) – Whether to access adata .raw.var or adata .var.

  • cmap (str) – Colormap to use.

  • fontsize (int) – Size of the text when plotting gene_sets.

  • adjust_text (bool) – Whether to automatically adjust text in order to reduce overlap.

  • legend_loc (Optional[str]) – Position of the legend. If None, don’t show the legend. Only used when gene_sets!=None.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • show (bool) – If False, return matplotlib.pyplot.Axes.

  • kwargs (Any) – Keyword arguments for scanpy.pl.scatter().

Return type

Optional[Axes]

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

Notes

This plot is based on the following notebook by Maren Büttner.

fit(keys=None, compute_absorption_probabilities=True, **kwargs)[source]

Run the pipeline.

Parameters
  • keys (Optional[Sequence]) – States for which to compute absorption probabilities.

  • compute_absorption_probabilities (bool) – Whether to compute absorption probabilities or just initial or terminal states.

  • kwargs – Keyword arguments.

Returns

Nothing, just makes available the following fields:

  • terminal_states_probabilities

  • terminal_states

  • absorption_probabilities

  • priming_degree

Return type

None

copy()[source]

Return a copy of self, including the underlying adata object.

Return type

BaseEstimator

write(fname, ext='pickle')[source]

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

Kernel

class cellrank.tl.kernels.Kernel(adata, backward=False, compute_cond_num=False, check_connectivity=False, **kwargs)[source]

A base class from which all kernels are derived.

These kernels read from a given AnnData object, usually the KNN graph and additional variables, to compute a weighted, directed graph. Every kernel object has a direction. The kernels defined in the derived classes are not strictly kernels in the mathematical sense because they often only take one input argument - however, they build on other functions which have computed a similarity based on two input arguments. The role of the kernels defined here is to add directionality to these symmetric similarity relations or to transform them.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

  • check_connectivity (bool) – Check whether the underlying KNN graph is connected.

  • kwargs (Any) – Keyword arguments which can specify key to be read from adata object.

property adata: anndata._core.anndata.AnnData

Annotated data object.

Returns

Annotated data object.

Return type

anndata.AnnData

property backward: bool

Direction of the process.

Return type

bool

compute_projection(basis='umap', key_added=None, copy=False)

Compute a projection of the transition matrix in the embedding.

Projections can only be calculated for kNN based kernels. The projected matrix can be then visualized as:

scvelo.pl.velocity_embedding(adata, vkey='T_fwd', basis='umap')
Parameters
  • basis (str) – Basis in adata .obsm for which to compute the projection.

  • key_added (Optional[str]) – If not None and copy=False, save the result to adata .obsm['{key_added}']. Otherwise, save the result to ‘T_fwd_{basis}’ or T_bwd_{basis}, depending on the direction.

  • copy (bool) – Whether to return the projection or modify adata inplace.

Return type

Optional[ndarray]

Returns

  • If copy=True, the projection array of shape (n_cells, n_components).

  • Otherwise, it modifies anndata.AnnData.obsm with a key based on key_added.

abstract compute_transition_matrix(*args, **kwargs)

Compute a transition matrix.

Parameters
  • args (Any) – Positional arguments.

  • kwargs (Any) – Keyword arguments.

Returns

Self.

Return type

cellrank.tl.kernels.KernelExpression

property condition_number: Optional[int]

Condition number of the transition matrix.

Return type

Optional[int]

abstract copy()

Return a copy of itself. Note that the underlying adata object is not copied.

Return type

KernelExpression

property kernels: List[cellrank.tl.kernels._base_kernel.Kernel]

Get the kernels of the kernel expression, except for constants.

Return type

List[Kernel]

property params: Dict[str, Any]

Parameters which are used to compute the transition matrix.

Return type

Dict[str, Any]

plot_random_walks(n_sims, max_iter=0.25, seed=None, successive_hits=0, start_ixs=None, stop_ixs=None, basis='umap', cmap='gnuplot', linewidth=1.0, linealpha=0.3, ixs_legend_loc=None, n_jobs=None, backend='loky', show_progress_bar=True, figsize=None, dpi=None, save=None, **kwargs)

Plot random walks in an embedding.

This method simulates random walks on the Markov chain defined though the corresponding transition matrix. The method is intended to give qualitative rather than quantitative insights into the transition matrix. Random walks are simulated by iteratively choosing the next cell based on the current cell’s transition probabilities.

Parameters
  • n_sims (int) – Number of random walks to simulate.

  • max_iter (Union[int, float]) – Maximum number of steps of a random walk. If a float, it can be specified as a fraction of the number of cells.

  • seed (Optional[int]) – Random seed.

  • successive_hits (int) – Number of successive hits in the stop_ixs required to stop prematurely.

  • start_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells from which to sample the starting points. If None, use all cells. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Ngn3 low EP', 'Ngn3 high EP']} means that starting points for random walks will be samples uniformly from the these clusters.

  • stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Alpha', 'Beta']} and succesive_hits=3 means that the random walk will stop prematurely after cells in the above specified clusters have been visited successively 3 times in a row.

  • basis (str) – Basis in anndata.AnnData.obsm to use as an embedding.

  • cmap (Union[str, LinearSegmentedColormap]) – Colormap for the random walk lines.

  • linewidth (float) – Width of the random walk lines.

  • linealpha (float) – Alpha value of the random walk lines.

  • ixs_legend_loc (Optional[str]) – Legend location for the start/top indices.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

None

Returns

  • None – Nothing, just plots the figure. Optionally saves it based on save.

  • For each random walk, the first/last cell is marked by the start/end colors of cmap.

plot_single_flow(cluster, cluster_key, time_key, clusters=None, time_points=None, min_flow=0, remove_empty_clusters=True, ascending=False, legend_loc='upper right out', alpha=0.8, xticks_step_size=1, figsize=None, dpi=None, save=None, show=True)

Visualize outgoing flow from a cluster of cells [Mittnenzweig et al., 2021].

Parameters
  • cluster (str) – Cluster for which to visualize outgoing compute_flow.

  • cluster_key (str) – Key in adata .obs where clustering is stored.

  • time_key (str) – Key in adata .obs where experimental time is stored.

  • clusters (Optional[Sequence[Any]]) – Visualize flow only for these clusters. If None, use all clusters.

  • time_points (Optional[Sequence[Union[float, int]]]) – Visualize flow only for these time points. If None, use all time points.

  • min_flow (float) – Only show flow edges with flow greater than this value. Flow values are always in [0, 1].

  • remove_empty_clusters (bool) – Whether to remove clusters with no incoming flow edges.

  • ascending (Optional[bool]) – Whether to sort the cluster by ascending or descending incoming flow. If None, use the order as in defined by clusters.

  • alpha (Optional[float]) – Alpha value for cell proportions.

  • xticks_step_size (Optional[int]) – Show only every n-th ticks on x-axis. If None, don’t show any ticks.

  • legend_loc (Optional[str]) – Position of the legend. If None, do not show the legend.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • show (bool) – If False, return matplotlib.pyplot.Axes.

Return type

Optional[Axes]

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

Notes

This function is a Python reimplementation of the following original R function with some minor stylistic differences. This function will not recreate the results from [Mittnenzweig et al., 2021], because there the Metacell model [Baran et al., 2019] was used to compute the flow, whereas here the transition matrix is used.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property transition_matrix: Union[numpy.ndarray, scipy.sparse.base.spmatrix]

Return row-normalized transition matrix.

If not present, it is computed iff all underlying kernels have been initialized.

Return type

Union[ndarray, spmatrix]

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

write_to_adata(key=None)

Write the transition matrix and parameters used for computation to the underlying adata object.

Parameters

key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’.

Returns

Updates the adata with the following fields:

  • .obsp['{key}'] - the transition matrix.

  • .uns['{key}_params'] - parameters used for calculation.

Return type

None

ExperimentalTime Kernel

class cellrank.tl.kernels.ExperimentalTimeKernel(adata, backward=False, time_key='exp_time', compute_cond_num=False)[source]

Kernel base class which computes directed transition probabilities based on experimental time.

Optionally, we apply a density correction as described in [Coifman et al., 2005], where we use the implementation of [Haghverdi et al., 2016].

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • backward (bool) – Direction of the process.

  • time_key (str) – Key in adata .obs where experimental time is stored. The experimental time can be of either of a numeric or an ordered categorical type.

  • compute_cond_num (bool) – Whether to compute condition number of the transition matrix. Note that this might be costly, since it does not use sparse implementation.

plot_single_flow(cluster, cluster_key, time_key=None, *args, **kwargs)[source]

Visualize outgoing flow from a cluster of cells [Mittnenzweig et al., 2021].

Parameters
  • cluster (str) – Cluster for which to visualize outgoing compute_flow.

  • cluster_key (str) – Key in adata .obs where clustering is stored.

  • time_key (Optional[str]) – Key in adata .obs where experimental time is stored.

  • clusters – Visualize flow only for these clusters. If None, use all clusters.

  • time_points – Visualize flow only for these time points. If None, use all time points.

  • min_flow – Only show flow edges with flow greater than this value. Flow values are always in [0, 1].

  • remove_empty_clusters – Whether to remove clusters with no incoming flow edges.

  • ascending – Whether to sort the cluster by ascending or descending incoming flow. If None, use the order as in defined by clusters.

  • alpha – Alpha value for cell proportions.

  • xticks_step_size – Show only every n-th ticks on x-axis. If None, don’t show any ticks.

  • legend_loc – Position of the legend. If None, do not show the legend.

  • figsize – Size of the figure.

  • dpi – Dots per inch.

  • save – Filename where to save the plot.

  • show – If False, return matplotlib.pyplot.Axes.

Return type

None

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

property experimental_time: pandas.core.series.Series

Experimental time.

Return type

Series

copy()[source]

Return a copy of self.

Return type

ExperimentalTimeKernel

property adata: anndata._core.anndata.AnnData

Annotated data object.

Returns

Annotated data object.

Return type

anndata.AnnData

property backward: bool

Direction of the process.

Return type

bool

compute_projection(basis='umap', key_added=None, copy=False)

Compute a projection of the transition matrix in the embedding.

Projections can only be calculated for kNN based kernels. The projected matrix can be then visualized as:

scvelo.pl.velocity_embedding(adata, vkey='T_fwd', basis='umap')
Parameters
  • basis (str) – Basis in adata .obsm for which to compute the projection.

  • key_added (Optional[str]) – If not None and copy=False, save the result to adata .obsm['{key_added}']. Otherwise, save the result to ‘T_fwd_{basis}’ or T_bwd_{basis}, depending on the direction.

  • copy (bool) – Whether to return the projection or modify adata inplace.

Return type

Optional[ndarray]

Returns

  • If copy=True, the projection array of shape (n_cells, n_components).

  • Otherwise, it modifies anndata.AnnData.obsm with a key based on key_added.

abstract compute_transition_matrix(*args, **kwargs)

Compute a transition matrix.

Parameters
  • args (Any) – Positional arguments.

  • kwargs (Any) – Keyword arguments.

Returns

Self.

Return type

cellrank.tl.kernels.KernelExpression

property condition_number: Optional[int]

Condition number of the transition matrix.

Return type

Optional[int]

property kernels: List[cellrank.tl.kernels._base_kernel.Kernel]

Get the kernels of the kernel expression, except for constants.

Return type

List[Kernel]

property params: Dict[str, Any]

Parameters which are used to compute the transition matrix.

Return type

Dict[str, Any]

plot_random_walks(n_sims, max_iter=0.25, seed=None, successive_hits=0, start_ixs=None, stop_ixs=None, basis='umap', cmap='gnuplot', linewidth=1.0, linealpha=0.3, ixs_legend_loc=None, n_jobs=None, backend='loky', show_progress_bar=True, figsize=None, dpi=None, save=None, **kwargs)

Plot random walks in an embedding.

This method simulates random walks on the Markov chain defined though the corresponding transition matrix. The method is intended to give qualitative rather than quantitative insights into the transition matrix. Random walks are simulated by iteratively choosing the next cell based on the current cell’s transition probabilities.

Parameters
  • n_sims (int) – Number of random walks to simulate.

  • max_iter (Union[int, float]) – Maximum number of steps of a random walk. If a float, it can be specified as a fraction of the number of cells.

  • seed (Optional[int]) – Random seed.

  • successive_hits (int) – Number of successive hits in the stop_ixs required to stop prematurely.

  • start_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells from which to sample the starting points. If None, use all cells. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Ngn3 low EP', 'Ngn3 high EP']} means that starting points for random walks will be samples uniformly from the these clusters.

  • stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Alpha', 'Beta']} and succesive_hits=3 means that the random walk will stop prematurely after cells in the above specified clusters have been visited successively 3 times in a row.

  • basis (str) – Basis in anndata.AnnData.obsm to use as an embedding.

  • cmap (Union[str, LinearSegmentedColormap]) – Colormap for the random walk lines.

  • linewidth (float) – Width of the random walk lines.

  • linealpha (float) – Alpha value of the random walk lines.

  • ixs_legend_loc (Optional[str]) – Legend location for the start/top indices.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

None

Returns

  • None – Nothing, just plots the figure. Optionally saves it based on save.

  • For each random walk, the first/last cell is marked by the start/end colors of cmap.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property transition_matrix: Union[numpy.ndarray, scipy.sparse.base.spmatrix]

Return row-normalized transition matrix.

If not present, it is computed iff all underlying kernels have been initialized.

Return type

Union[ndarray, spmatrix]

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

write_to_adata(key=None)

Write the transition matrix and parameters used for computation to the underlying adata object.

Parameters

key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’.

Returns

Updates the adata with the following fields:

  • .obsp['{key}'] - the transition matrix.

  • .uns['{key}_params'] - parameters used for calculation.

Return type

None

TransportMap Kernel

class cellrank.tl.kernels.TransportMapKernel(*args, **kwargs)[source]

Kernel base class which computes transition matrix based on transport maps for consecutive time pairs.

property transport_maps: Optional[Dict[Tuple[float, float], anndata._core.anndata.AnnData]]

Transport maps for consecutive time pairs.

Return type

Optional[Dict[Tuple[float, float], AnnData]]

property adata: anndata._core.anndata.AnnData

Annotated data object.

Returns

Annotated data object.

Return type

anndata.AnnData

property backward: bool

Direction of the process.

Return type

bool

compute_projection(basis='umap', key_added=None, copy=False)

Compute a projection of the transition matrix in the embedding.

Projections can only be calculated for kNN based kernels. The projected matrix can be then visualized as:

scvelo.pl.velocity_embedding(adata, vkey='T_fwd', basis='umap')
Parameters
  • basis (str) – Basis in adata .obsm for which to compute the projection.

  • key_added (Optional[str]) – If not None and copy=False, save the result to adata .obsm['{key_added}']. Otherwise, save the result to ‘T_fwd_{basis}’ or T_bwd_{basis}, depending on the direction.

  • copy (bool) – Whether to return the projection or modify adata inplace.

Return type

Optional[ndarray]

Returns

  • If copy=True, the projection array of shape (n_cells, n_components).

  • Otherwise, it modifies anndata.AnnData.obsm with a key based on key_added.

abstract compute_transition_matrix(*args, **kwargs)

Compute a transition matrix.

Parameters
  • args (Any) – Positional arguments.

  • kwargs (Any) – Keyword arguments.

Returns

Self.

Return type

cellrank.tl.kernels.KernelExpression

property condition_number: Optional[int]

Condition number of the transition matrix.

Return type

Optional[int]

copy()

Return a copy of self.

Return type

ExperimentalTimeKernel

property experimental_time: pandas.core.series.Series

Experimental time.

Return type

Series

property kernels: List[cellrank.tl.kernels._base_kernel.Kernel]

Get the kernels of the kernel expression, except for constants.

Return type

List[Kernel]

property params: Dict[str, Any]

Parameters which are used to compute the transition matrix.

Return type

Dict[str, Any]

plot_random_walks(n_sims, max_iter=0.25, seed=None, successive_hits=0, start_ixs=None, stop_ixs=None, basis='umap', cmap='gnuplot', linewidth=1.0, linealpha=0.3, ixs_legend_loc=None, n_jobs=None, backend='loky', show_progress_bar=True, figsize=None, dpi=None, save=None, **kwargs)

Plot random walks in an embedding.

This method simulates random walks on the Markov chain defined though the corresponding transition matrix. The method is intended to give qualitative rather than quantitative insights into the transition matrix. Random walks are simulated by iteratively choosing the next cell based on the current cell’s transition probabilities.

Parameters
  • n_sims (int) – Number of random walks to simulate.

  • max_iter (Union[int, float]) – Maximum number of steps of a random walk. If a float, it can be specified as a fraction of the number of cells.

  • seed (Optional[int]) – Random seed.

  • successive_hits (int) – Number of successive hits in the stop_ixs required to stop prematurely.

  • start_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells from which to sample the starting points. If None, use all cells. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Ngn3 low EP', 'Ngn3 high EP']} means that starting points for random walks will be samples uniformly from the these clusters.

  • stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str]]], None]) – Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as either a dict with a key corresponding to cluster key in anndata.AnnData.obs and values to clusters or just a sequence of cell ids in anndata.AnnData.obs_names. For example {'clusters': ['Alpha', 'Beta']} and succesive_hits=3 means that the random walk will stop prematurely after cells in the above specified clusters have been visited successively 3 times in a row.

  • basis (str) – Basis in anndata.AnnData.obsm to use as an embedding.

  • cmap (Union[str, LinearSegmentedColormap]) – Colormap for the random walk lines.

  • linewidth (float) – Width of the random walk lines.

  • linealpha (float) – Alpha value of the random walk lines.

  • ixs_legend_loc (Optional[str]) – Legend location for the start/top indices.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

  • figsize (Optional[Tuple[float, float]]) – Size of the figure.

  • dpi (Optional[int]) – Dots per inch.

  • save (Union[str, Path, None]) – Filename where to save the plot.

  • kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

None

Returns

  • None – Nothing, just plots the figure. Optionally saves it based on save.

  • For each random walk, the first/last cell is marked by the start/end colors of cmap.

plot_single_flow(cluster, cluster_key, time_key=None, *args, **kwargs)

Visualize outgoing flow from a cluster of cells [Mittnenzweig et al., 2021].

Parameters
  • cluster (str) – Cluster for which to visualize outgoing compute_flow.

  • cluster_key (str) – Key in adata .obs where clustering is stored.

  • time_key (Optional[str]) – Key in adata .obs where experimental time is stored.

  • clusters – Visualize flow only for these clusters. If None, use all clusters.

  • time_points – Visualize flow only for these time points. If None, use all time points.

  • min_flow – Only show flow edges with flow greater than this value. Flow values are always in [0, 1].

  • remove_empty_clusters – Whether to remove clusters with no incoming flow edges.

  • ascending – Whether to sort the cluster by ascending or descending incoming flow. If None, use the order as in defined by clusters.

  • alpha – Alpha value for cell proportions.

  • xticks_step_size – Show only every n-th ticks on x-axis. If None, don’t show any ticks.

  • legend_loc – Position of the legend. If None, do not show the legend.

  • figsize – Size of the figure.

  • dpi – Dots per inch.

  • save – Filename where to save the plot.

  • show – If False, return matplotlib.pyplot.Axes.

Return type

None

Returns

  • matplotlib.pyplot.Axes – The axis object if show=False.

  • None – Nothing, just plots the figure. Optionally saves it based on save.

static read(fname)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.

Returns

The deserialized object.

Return type

typing.Any

property transition_matrix: Union[numpy.ndarray, scipy.sparse.base.spmatrix]

Return row-normalized transition matrix.

If not present, it is computed iff all underlying kernels have been initialized.

Return type

Union[ndarray, spmatrix]

write(fname, ext='pickle')

Serialize self to a file.

Parameters
  • fname (Union[str, Path]) – Filename where to save the object.

  • ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Returns

Nothing, just writes itself to a file using pickle.

Return type

None

write_to_adata(key=None)

Write the transition matrix and parameters used for computation to the underlying adata object.

Parameters

key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key is set to ‘T_bwd’ if backward is True, else ‘T_fwd’.

Returns

Updates the adata with the following fields:

  • .obsp['{key}'] - the transition matrix.

  • .uns['{key}_params'] - parameters used for calculation.

Return type

None

Similarity Scheme

class cellrank.tl.kernels.SimilaritySchemeABC[source]

Base class for all similarity schemes.

abstract __call__(v, D, softmax_scale=1.0)[source]

Compute transition probability of a cell to its nearest neighbors using RNA velocity.

Parameters
  • v (ndarray) – Array of shape (n_genes,) or (n_neighbors, n_genes) containing the velocity vector(s). The second case is used for the backward process.

  • D (ndarray) – Array of shape (n_neighbors, n_genes) corresponding to the transcriptomic displacement of the current cell with respect to ist nearest neighbors.

  • softmax_scale (float) – Scaling factor for the softmax function.

Returns

The probability and logits arrays of shape (n_neighbors,).

Return type

numpy.ndarray, numpy.ndarray

Threshold Scheme

class cellrank.tl.kernels.ThresholdSchemeABC[source]

Base class for all connectivity biasing schemes.

abstract __call__(cell_pseudotime, neigh_pseudotime, neigh_conn, **kwargs)[source]

Calculate biased connections for a given cell.

Parameters
  • cell_pseudotime (float) – Pseudotime of the current cell.

  • neigh_pseudotime (ndarray) – Array of shape (n_neighbors,) containing pseudotimes of neighbors.

  • neigh_conn (ndarray) – Array of shape (n_neighbors,) containing connectivities of the current cell and its neighbors.

Returns

Return type

Array of shape (n_neighbors,) containing the biased connectivities.

bias_knn(conn, pseudotime, n_jobs=None, backend='loky', show_progress_bar=True, **kwargs)[source]

Bias cell-cell connectivities of a KNN graph.

Parameters
  • conn (csr_matrix) – Sparse matrix of shape (n_cells, n_cells) containing the nearest neighbor connectivities.

  • pseudotime (ndarray) – Pseudotemporal ordering of cells.

  • show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

  • n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

  • backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

Returns

Return type

The biased connectivities.

BaseModel

class cellrank.ul.models.BaseModel(adata, model)[source]

Base class for all model classes.

Parameters
  • adata (anndata.AnnData) – Annotated data object.

  • model (Any) – The underlying model that is used for fitting and prediction.

property prepared

Whether the model is prepared for fitting.

property adata: cellrank.ul.models._base_model.AnnData

Annotated data object.

Returns

adata – Annotated data object.

Return type

anndata.AnnData

property model: Any

The underlying model.

Return type

Any

property x_all: numpy.ndarray

Unfiltered independent variables of shape (n_cells, 1).

Return type

ndarray

property y_all: numpy.ndarray

Unfiltered dependent variables of shape (n_cells, 1).

Return type

ndarray

property w_all: numpy.ndarray

Unfiltered weights of shape (n_cells,).

Return type

ndarray

property x: numpy.ndarray

Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property y: numpy.ndarray

Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

Return type

ndarray

property w: numpy.ndarray

Filtered weights of shape (n_filtered_cells,) used for fitting.

Return type

ndarray

property x_test: numpy.ndarray

Independent variables of shape (n_samples, 1) used for prediction.

Return type

ndarray

property y_test: numpy.ndarray

Prediction values of shape (n_samples,) for x_test.

Return type

ndarray

property x_hat: numpy.ndarray

Filtered independent variables used when calculating default confidence interval, usually same as x.

Return type

ndarray

property y_hat: numpy.ndarray

Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

ndarray

property conf_int: numpy.ndarray

Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

ndarray

prepare(gene, lineage, backward=False, time_range=None, data_key='X', time_key='latent_time', use_raw=False, threshold=None, weight_threshold=(0.01, 0.01), filter_cells=None, n_test_points=200)[source]

Prepare the model to be ready for fitting.

Parameters
  • gene (str) – Gene in adata .var_names or in adata .raw.var_names.

  • lineage (Optional[str]) – Name of a lineage in adata .obsm['{lineage_key}']. If None, all weights will be set to 1.

  • backward (bool) – Direction of the process.

  • time_range (Union[float, Tuple[float, float], None]) –

    Specify start and end times:

    • If a tuple, it specifies the minimum and maximum pseudotime. Both values can be None, in which case the minimum is the earliest pseudotime and the maximum is automatically determined.

    • If a float, it specifies the maximum pseudotime.

  • data_key (str) – Key in adata .layers or ‘X’ for adata .X. If use_raw=True, it’s always set to ‘X’.

  • time_key (str) – Key in adata .obs where the pseudotime is stored.

  • use_raw (bool) – Whether to access adata .raw or not.

  • threshold (Optional[float]) – Consider only cells with weights > threshold when estimating the test endpoint. If None, use the median of the weights.

  • weight_threshold (Union[float, Tuple[float, float]]) – Set all weights below weight_threshold to weight_threshold if a float, or to the second value, if a tuple.

  • filter_cells (Optional[float]) – Filter out all cells with expression values lower than this threshold.

  • n_test_points (int) – Number of test points. If None, use the original points based on threshold.

Returns

Nothing, but updates the following fields:

  • x - Filtered independent variables of shape (n_filtered_cells, 1) used for fitting.

  • y - Filtered dependent variables of shape (n_filtered_cells, 1) used for fitting.

  • w - Filtered weights of shape (n_filtered_cells,) used for fitting.

  • x_all - Unfiltered independent variables of shape (n_cells, 1).

  • y_all - Unfiltered dependent variables of shape (n_cells, 1).

  • w_all - Unfiltered weights of shape (n_cells,).

  • x_test - Independent variables of shape (n_samples, 1) used for prediction.

  • prepared - Whether the model is prepared for fitting.

Return type

None

abstract fit(x=None, y=None, w=None, **kwargs)[source]

Fit the model.

Parameters
  • x (Optional[ndarray]) – Independent variables, array of shape (n_samples, 1). If None, use x.

  • y (Optional[ndarray]) – Dependent variables, array of shape (n_samples, 1). If None, use y.

  • w (Optional[ndarray]) – Optional weights of x, array of shape (n_samples,). If None, use w.

  • kwargs – Keyword arguments for underlying model’s fitting function.

Returns

Fits the model and returns self.

Return type

cellrank.ul.models.BaseModel

abstract predict(x_test=None, key_added='_x_test', **kwargs)[source]

Run the prediction.

Parameters
  • x_test (Optional[ndarray]) – Array of shape (n_samples,) used for prediction. If None, use x_test.

  • key_added (Optional[str]) – Attribute name where to save the x_test for later use. If None, don’t save it.

  • kwargs – Keyword arguments for underlying model’s prediction method.

Returns

Updates and returns the following:

  • y_test - Prediction values of shape (n_samples,) for x_test.

Return type

numpy.ndarray

abstract confidence_interval(x_test=None, **kwargs)[source]

Calculate the confidence interval.

Use default_confidence_interval() function if underlying model has not method for confidence interval calculation.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

Return type

numpy.ndarray

default_confidence_interval(x_test=None, **kwargs)[source]

Calculate the confidence interval, if the underlying model has no method for it.

This formula is taken from [DeSalvo, 1970], eq. 5.

Parameters
Returns

Updates the following fields:

  • conf_int - Array of shape (n_samples, 2) containing the lower and upper bounds of the confidence interval.

  • x_hat - Filtered independent variables used when calculating default confidence interval, usually same as x.

  • y_hat - Filtered dependent variables used when calculating default confidence interval, usually same as y.

Return type

numpy.ndarray

plot(figsize=(8, 5), same_plot=False, hide_cells=False, perc=None, abs_prob_cmap=<matplotlib.colors.ListedColormap object>, cell_color=None, lineage_color='black', alpha=0.8, lineage_alpha=0.2, title=None, size=15, lw=2, cbar=True, margins=0.015, xlabel='pseudotime', ylabel='expression', conf_int=True, lineage_probability=False, lineage_probability_conf_int=False, lineage_probability_color=None, obs_legend_loc='best', dpi=None, fig=None, ax=None, return_fig=False, save=None, **kwargs)[source]

Plot the smoothed gene expression.

Parameters
  • figsize (Tuple[float, float]) – Size of the figure.

  • same_plot (bool) – Whether to plot all trends in the same plot.

  • hide_cells (bool) – Whether to hide the cells.

  • perc (Optional[Tuple[float, float]]) – Percentile by which to clip the absorption probabilities.

  • abs_prob_cmap (ListedColormap) – Colormap to use when coloring in the absorption probabilities.

  • cell_color (Optional[str]) – Key in anndata.AnnData.obs or anndata.AnnData.var_names used for coloring the cells.

  • lineage_color (str) – Color for the lineage.

  • alpha (float) – Alpha channel for cells.

  • lineage_alpha (float) – Alpha channel for lineage confidence intervals.

  • title (Optional[str]) – Title of the plot.

  • size (int) – Size of the points.

  • lw (float) – Line width for the smoothed values.

  • cbar (bool) – Whether to show colorbar.

  • margins (float) – Margins around the plot.

  • xlabel (str) – Label on the x-axis.

  • ylabel (str) – Label on the y-axis.

  • conf_int (bool) – Whether to show the confidence interval.

  • lineage_probability (bool) – Whether to show smoothed lineage probability as a dashed line. Note that this will require 1 additional model fit.

  • lineage_probability_conf_int (Union[bool, float]) – Whether to compute and show smoothed lineage probability confidence interval. If self is cellrank.ul.models.GAMR, it can also specify the confidence level, the default is 0.95. Only used when show_lineage_probability=True.

  • lineage_probability_color (Optional[str]) – Color to use when plotting the smoothed lineage_probability. If None, it’s the same as lineage_color. Only used when show_lineage_probability=True.

  • obs_legend_loc (Optional[str]) – Location of the legend when cell_color corresponds to a categorical variable.

  • dpi (Optional[int]) – Dots per inch.

  • fig (Optional[Figure]) – Figure to use, if None, create a new one.

  • ax (matplotlib.axes.Axes) – Ax to use, if None, create a new one.

  • return_fig (bool) – If True, return the figure object.

  • save (Optional[str]) – Filename where to save the plot. If None, just shows the plots.

  • kwargs – Keyword arguments for matplotlib.axes.Axes.legend(), e.g. to disable the legend, specify loc=None. Only available when show_lineage_probability=True.

Returns

Nothing, just plots the figure. Optionally saves it based on save.

Return type

None

abstract copy()[source]

Return a copy of self.

Return type

BaseModel

Lineage

class cellrank.tl.Lineage(input_array: numpy.ndarray, *, names: Iterable[str], colors: Optional[Iterable[cellrank.tl._lineage.ColorLike]] = None)[source]

Lightweight numpy.ndarray wrapper that adds names and colors.

Parameters
  • input_array – Input array containing lineage probabilities, each lineage being stored in a column.

  • names – Names of the lineages.

  • colors – Colors of the lineages.

property names: numpy.ndarray

Lineage names. Must be unique.

Return type

ndarray

property colors: numpy.ndarray

Lineage colors.

Return type

ndarray

property X: numpy.ndarray

Convert self to numpy array, losing names and colors.

Return type

ndarray

property T

Transpose of self.

view(dtype=None, type=None)[source]

Return a view of self.

Return type

LineageView

priming_degree(method='kl_divergence', early_cells=None)[source]

Compute the degree of lineage priming.

This method computes how naive vs. committed each individual cell is. It returns a score where 0 stands for naive and 1 stands for committed.

Parameters
  • method (Literal[‘kl_divergence’, ‘entropy’]) –

    The method used to compute the degree of lineage priming. Valid options are:

    • ’kl_divergence’: as in [Velten et al., 2017], computes KL-divergence between the fate probabilities of a cell and the average fate probabilities. Computation of average fate probabilities can be restricted to a set of user-defined early_cells.

    • ’entropy’: as in [Setty et al., 2019], computes entropy over a cell’s fate probabilities.

  • early_cells (Optional[ndarray]) – Cell ids or a mask marking early cells. If None, use all cells. Only used when method='kl_divergence'.

Returns

Return type

The priming degree.

plot_pie(reduction, title=None, legend_loc='on data', legend_kwargs=mappingproxy({}), figsize=None, dpi=None, save=None, **kwargs)[source]

Plot a pie chart visualizing aggregated lineage probabilities.

Parameters
  • reduction (