Classes 

Returns

Nothing, just updates the following fields:

macrostates - Macrostates of the transition matrix.
macrostates_memberships - Macrostate membership matrix.
coarse_T - Coarse-grained transition matrix.
coarse_initial_distribution - Coarse-grained initial distribution.
coarse_stationary_distribution - Coarse-grained stationary distribution.
schur_vectors - Real Schur vectors of the transition matrix.
schur_matrix - Schur matrix.
eigendecomposition - Eigendecomposition of transition_matrix.

predict(method=TermStatesMethod.STABILITY, n_cells=30, alpha=1, stability_threshold=0.96, n_states=None)[source]

Automatically select terminal states from macrostates.

Parameters

method (Literal[‘stability’, ‘top_n’, ‘eigengap’, ‘eigengap_coarse’]) –
How to select the terminal states. Valid option are:
- ’eigengap’ - select the number of states based on the eigengap of transition_matrix.
- ’eigengap_coarse’ - select the number of states based on the eigengap of the diagonal of coarse_T.
- ’top_n’ - select top n_states based on the probability of the diagonal of coarse_T.
- ’stability’ - select states which have a stability >= stability_threshold. The stability is given by the diagonal elements of coarse_T.
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. Only used when method = 'eigengap' or method = 'eigengap_coarse'.
stability_threshold (float) – Threshold used when method = 'stability'.
n_states (Optional[int]) – Number of states used when method = 'top_n'.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_memberships - Terminal state membership matrix.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

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

Manually select terminal states from macrostates.

Parameters

names (Union[str, Sequence[str], Mapping[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.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.
terminal_states_probabilities_memberships - Terminal state membership matrix.

rename_terminal_states(new_names)[source]

Rename categories in terminal_states.

Parameters

new_names (Mapping[str, str]) – Mapping where keys corresponds to the old names and the values to the new names. The new names must be unique.

Return type

Returns

Nothing, just updates the names of:

terminal_states - Categorical annotation of terminal states.
terminal_states_memberships - Terminal state membership matrix.

fit(n_states=None, n_cells=30, cluster_key=None, **kwargs)[source]

Prepare self for terminal states prediction.

Parameters

n_states (Union[int, Sequence[int], None]) – Number of macrostates. If a typing.Sequence, use the minChi criterion [Reuter et al., 2018]. If None, use the eigengap heuristic.
n_cells (Optional[int]) – Number of most likely cells from each macrostate to select.
cluster_key (Optional[str]) – If a key to cluster labels is given, names and colors of the states will be associated with the clusters.
kwargs (Any) – Keyword arguments for compute_schur().

Return type

GPCCA

Returns

Nothing, just updates the following fields:

macrostates - Macrostates of the transition matrix.
macrostates_memberships - Macrostate membership matrix.
coarse_T - Coarse-grained transition matrix.
coarse_initial_distribution - Coarse-grained initial distribution.
coarse_stationary_distribution - Coarse-grained stationary distribution.
schur_vectors - Real Schur vectors of the transition matrix.
schur_matrix - Schur matrix.
eigendecomposition - Eigendecomposition of transition_matrix.

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

show_stationary_dist (bool) – Whether to show coarse_stationary_distribution, if present.
show_initial_dist (bool) – Whether to show coarse_initial_distribution.
cmap (Union[str, ListedColormap]) – Colormap to use.
xtick_rotation (float) – Rotation of ticks on the x-axis.
annotate (bool) – Whether to display the text on each cell.
show_cbar (bool) – Whether to show colorbar.
title (Optional[str]) – Title of the figure.
figsize (Tuple[float, float]) – Size of the figure.
dpi (int) – Dots per inch.
save (Union[str, Path, None]) – Filename where to save the plot.
text_kwargs (Mapping[str, Any]) – Keyword arguments for matplotlib.pyplot.text().
kwargs (Any) – Keyword arguments for matplotlib.pyplot.imshow().

Return type

Returns

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

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 anndata.AnnData.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

The axes object, if show = False. Nothing, just plots the figure. Optionally saves it based on save.

plot_macrostates(states=None, color=None, discrete=False, mode=PlotMode.EMBEDDING, time_key='latent_time', same_plot=True, title=None, cmap='viridis', **kwargs)

Plot continuous or categorical observations in an embedding or along pseudotime.

Parameters

states (Union[str, Sequence[str], None]) – States to plot.
color (Optional[str]) – Key in anndata.AnnData.obs.
discrete (bool) – Whether to plot the data as continuous or discrete observations. If the data cannot be plotted as continuous observations, it will be plotted as discrete.
mode (Literal[‘embedding’, ‘time’]) –
Valid options are:
- ’embedding’ - plot the embedding while coloring in continuous or categorical observations.
- ’time’ - plot the pseudotime on x-axis and the probabilities/memberships on y-axis.
time_key (str) – Key in anndata.AnnData.obs where pseudotime is stored. Only used when mode = 'time'.
title (Union[str, Sequence[str], None]) – Title of the plot(s).
same_plot (bool) – Whether to plot the data on the same plot or not. Only use when mode = 'embedding'. If True and discrete = False, color is ignored.
cmap (str) – Colormap for continuous data.
kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

Returns

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

plot_terminal_states(states=None, color=None, discrete=False, mode=PlotMode.EMBEDDING, time_key='latent_time', same_plot=True, title=None, cmap='viridis', **kwargs)

Plot continuous or categorical observations in an embedding or along pseudotime.

Parameters

states (Union[str, Sequence[str], None]) – States to plot.
color (Optional[str]) – Key in anndata.AnnData.obs.
discrete (bool) – Whether to plot the data as continuous or discrete observations. If the data cannot be plotted as continuous observations, it will be plotted as discrete.
mode (Literal[‘embedding’, ‘time’]) –
Valid options are:
- ’embedding’ - plot the embedding while coloring in continuous or categorical observations.
- ’time’ - plot the pseudotime on x-axis and the probabilities/memberships on y-axis.
time_key (str) – Key in anndata.AnnData.obs where pseudotime is stored. Only used when mode = 'time'.
title (Union[str, Sequence[str], None]) – Title of the plot(s).
same_plot (bool) – Whether to plot the data on the same plot or not. Only use when mode = 'embedding'. If True and discrete = False, color is ignored.
cmap (str) – Colormap for continuous data.
kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

Returns

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

property absorption_probabilities: Optional[cellrank.tl._lineage.Lineage]

Absorption probabilities.

Informally, given a (finite, discrete) Markov chain with a set of transient states \(T\) and a set of absorbing states \(A\), the absorption probability for cell \(i\) from \(T\) to reach cell \(j\) from \(R\) is the probability that a random walk initialized in \(i\) will reach absorbing state \(j\).

In our context, states correspond to cells, in particular, absorbing states correspond to cells in terminal states.

Return type: Optional[Lineage]

property absorption_times: Optional[pandas.core.frame.DataFrame]

Mean and variance of the time until absorption.

Related to conditional mean first passage times. Corresponds to the expectation of the time until absorption, depending on initialization, and the variance.

Return type: Optional[DataFrame]

property adata: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData

property backward: bool

Direction of kernel.

Return type: bool

compute_absorption_probabilities(keys=None, 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.

For each cell, this computes the probability of being absorbed in any of the terminal_states. In particular, this corresponds to the probability that a random walk initialized in transient cell \(i\) will reach any cell from a fixed transient state before reaching a cell from any other transient state.

Parameters

keys (Optional[Sequence[str]]) – Terminal states for which to compute the absorption probabilities. If None, use all states defined in terminal_states.
solver (Union[str, Literal[‘direct’, ‘gmres’, ‘lgmres’, ‘bicgstab’, ‘gcrotmk’]]) –
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[Literal[‘all’], Sequence[Union[str, Sequence[str]]], Dict[Union[str, Sequence[str]], Literal[‘mean’, ‘var’]], 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 explicitly.

It might be beneficial to disable the progress bar as show_progress_bar = False because of many solves.
n_jobs (Optional[int]) – Number of parallel jobs to use when using an iterative solver.
backend (Literal[‘loky’, ‘multiprocessing’, ‘threading’]) – Which backend to use for multiprocessing. See joblib.Parallel for valid options.
show_progress_bar (bool) – Whether to show progress bar. Only used when solver != 'direct'.
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 valid options, see here. We recommend the ‘ilu’ preconditioner for badly conditioned problems.

Return type

Returns

Nothing, just updates the following fields:

absorption_probabilities - Absorption probabilities.
absorption_times - Mean and variance of the time until absorption. Only if time_to_absorption is specified.

compute_eigendecomposition(k=20, which='LR', alpha=1.0, 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 eigenvectors or eigenvalues to compute.
which (Literal[‘LR’, ‘LM’]) –
How to sort the eigenvalues. Valid option are:
- ’LR’ - the largest real part.
- ’LM’ - the 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) – Whether to compute only eigenvalues.
ncv (Optional[int]) – Number of Lanczos vectors generated.

Return type

Returns

Nothing, just updates the following field:

eigendecomposition - Eigendecomposition of transition_matrix.

compute_lineage_drivers(lineages=None, method=TestMethod.FISCHER, cluster_key=None, clusters=None, layer=None, use_raw=False, confidence_level=0.95, n_perms=1000, seed=None, **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]) – Lineage names from absorption_probabilities. If None, use all lineages.
method (Literal[‘fischer’, ‘perm_test’]) –
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 anndata.AnnData.obs to obtain cluster annotations. These are considered for clusters.
clusters (Union[str, Sequence, None]) – Restrict the correlations to these clusters.
layer (Optional[str]) – Key from anndata.AnnData.layers from which to get the expression. If None or ‘X’, use anndata.AnnData.X.
use_raw (bool) – Whether or not to use anndata.AnnData.raw to correlate gene expression.
confidence_level (float) – Confidence level for the confidence interval calculation. Must be in interval [0, 1].
n_perms (int) – Number of permutations to use when method = 'perm_test'.
seed (Optional[int]) – Random seed when method = 'perm_test'.
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

DataFrame

Returns

Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, one 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.

Also updates the following field:

lineage_drivers - the same pandas.DataFrame as described above.

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

Compute the degree of lineage priming.

It returns a score in [0, 1] 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'. If a dict, the key specifies a cluster key in anndata.AnnData.obs and the values specify cluster labels containing early cells.

Return type

Series

Returns

The priming degree.

Also updates the following field:

priming_degree - Priming degree.

compute_schur(n_components=10, initial_distribution=None, method='krylov', which='LR', alpha=1.0)

Compute Schur decomposition.

Parameters

n_components (int) – Number of Schur vectors to compute.
initial_distribution (Optional[ndarray]) – Input distribution over all cells. If None, uniform distribution is used.
method (Literal[‘krylov’, ‘brandts’]) –
Method for calculating the Schur vectors. Valid options are:
- ’krylov’ - an iterative procedure that computes a partial, sorted Schur decomposition for large, sparse matrices.
- ’brandts’ - full sorted Schur decomposition of a dense matrix.
For benefits of each method, see pygpcca.GPCCA.
which (Literal[‘LR’, ‘LM’]) –
How to sort the eigenvalues. Valid option are:
- ’LR’ - the largest real part.
- ’LM’ - the largest magnitude.
alpha (float) – Used to compute the eigengap. alpha is the weight given to the deviation of an eigenvalue from one.

Returns

Nothing, just updates the following fields:

schur_vectors - Real Schur vectors of the transition matrix.
schur_matrix - Schur matrix.
eigendecomposition - Eigendecomposition of transition_matrix.

compute_terminal_states(*args, **kwargs)

Compute terminal states of the process.

This is an alias for predict().

Parameters

args (Any) – Positional arguments.
kwargs (Any) – Keyword arguments arguments.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

copy(*, deep=False)

Return a copy of self.

Parameters: deep (bool) – Whether to return a deep copy or not. If True, this also copies the adata.
Return type: BaseEstimator
Returns: A copy of self.

property eigendecomposition: Optional[Dict[str, Any]]

Eigendecomposition of transition_matrix.

For non-symmetric real matrices, left and right eigenvectors will in general be different and complex. We compute both left and right eigenvectors.

Return type

Optional[Dict[str, Any]]

Returns

A dictionary with the following keys:

’D’ - the eigenvalues.
’eigengap’ - the eigengap.
’params’ - parameters used for the computation.
’V_l’ - left eigenvectors (optional).
’V_r’ - right eigenvectors (optional).
’stationary_dist’ - stationary distribution of transition_matrix, if present.

classmethod from_adata(adata, obsp_key)

Deserialize self from anndata.AnnData.

Parameters

adata (anndata.AnnData) – Annotated data object.
obsp_key (str) – Key in anndata.AnnData.obsp where the transition matrix is stored.

Return type

Returns

The deserialized object.

property kernel: cellrank.tl._mixins._kernel.KernelExpression

Underlying kernel expression.

Return type: ~KernelExpression

property lineage_drivers: Optional[pandas.core.frame.DataFrame]

Potential lineage drivers.

Computes Pearson correlation of each gene with fate probabilities for every terminal state. High Pearson correlation indicates potential lineage drivers. Also computes p-values and confidence intervals.

Return type

Optional[DataFrame]

Returns

Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, one 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.

property params: Dict[str, Any]

Estimator parameters.

Return type: Dict[str, Any]

plot_absorption_probabilities(states=None, color=None, discrete=False, mode=PlotMode.EMBEDDING, time_key='latent_time', same_plot=True, title=None, cmap='viridis', **kwargs)

Plot continuous or categorical observations in an embedding or along pseudotime.

Parameters

states (Union[str, Sequence[str], None]) – States to plot.
color (Optional[str]) – Key in anndata.AnnData.obs.
discrete (bool) – Whether to plot the data as continuous or discrete observations. If the data cannot be plotted as continuous observations, it will be plotted as discrete.
mode (Literal[‘embedding’, ‘time’]) –
Valid options are:
- ’embedding’ - plot the embedding while coloring in continuous or categorical observations.
- ’time’ - plot the pseudotime on x-axis and the probabilities/memberships on y-axis.
time_key (str) – Key in anndata.AnnData.obs where pseudotime is stored. Only used when mode = 'time'.
title (Union[str, Sequence[str], None]) – Title of the plot(s).
same_plot (bool) – Whether to plot the data on the same plot or not. Only use when mode = 'embedding'. If True and discrete = False, color is ignored.
cmap (str) – Colormap for continuous data.
kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

Returns

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

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 access in anndata.AnnData.raw or not.
title_fmt (str) – Title format. Can include {gene}, {pval}, {qval} or {corr}, which will be substituted with the actual values.
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

Returns

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

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 anndata.AnnData.var or anndata.AnnData.varm, preferring for the former.
gene_sets (Optional[Dict[str, Sequence[str]]]) – Gene sets annotations of the form {‘gene_set_name’: [‘gene_1’, ‘gene_2’], …}.
gene_sets_colors (Optional[Sequence[str]]) – 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 anndata.AnnData.raw or not.
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

The axes object, if show = False. Nothing, just plots the figure. Optionally saves it based on save.

Notes

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

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

Plot the Schur matrix.

Parameters

title (Optional[str]) – Title of the figure.
cmap (str) – Colormap to use.
figsize (Optional[Tuple[float, float]]) – Size of the figure.
dpi (Optional[float]) – Dots per inch.
save (Union[str, Path, None]) – Filename where to save the plot.
kwargs (Any) – Keyword arguments for seaborn.heatmap().

Returns

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

plot_spectrum(n=None, real_only=False, show_eigengap=True, show_all_xticks=True, legend_loc=None, title=None, marker='.', figsize=(5, 5), dpi=100, save=None, **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.
marker (str) – Marker symbol used, valid options can be found in matplotlib.markers.
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.
kwargs (Any) – Keyword arguments for matplotlib.pyplot.scatter().

Return type

Returns

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

property priming_degree: Optional[pandas.core.series.Series]

Priming degree.

Given a cell \(i\) and a set of terminal states, this quantifies how committed vs. naive cell \(i\) is, i.e. its degree of pluripotency. Low values correspond to naive cells (high degree of pluripotency), high values correspond to committed cells (low degree of pluripotency).

Return type: Optional[Series]

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property schur_matrix: Optional[numpy.ndarray]

Schur matrix.

The real Schur decomposition is a generalization of the Eigendecomposition and can be computed for any real-valued, square matrix \(A\). It is given by \(A = Q R Q^T\), where \(Q\) contains the real Schur vectors and \(R\) is the Schur matrix. \(Q\) is orthogonal and \(R\) is quasi-upper triangular with 1x1 and 2x2 blocks on the diagonal. If PETSc and SLEPc are installed, only the leading Schur vectors are computed.

Return type: Optional[ndarray]

property schur_vectors: Optional[numpy.ndarray]

Real Schur vectors of the transition matrix.

The real Schur decomposition is a generalization of the Eigendecomposition and can be computed for any real-valued, square matrix \(A\). It is given by \(A = Q R Q^T\), where \(Q\) contains the real Schur vectors and \(R\) is the Schur matrix. \(Q\) is orthogonal and \(R\) is quasi-upper triangular with 1x1 and 2x2 blocks on the diagonal. If PETSc and SLEPc are installed, only the leading Schur vectors are computed.

Return type: Optional[ndarray]

set_terminal_states(labels, cluster_key=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 a 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.AnnData.obs_names. If only 1 key is provided, values should correspond to terminal state clusters if a categorical pandas.Series can be found in anndata.AnnData.obs.
cluster_key (Optional[str]) – Key in anndata.AnnData.obs in order to associate names and colors with terminal_states. Each terminal state will be given the name and color corresponding to the cluster it mostly overlaps with.
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.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

property shape: Tuple[int, int]

Shape of the kernel.

Return type: Tuple[int, int]

property terminal_states: Optional[pandas.core.series.Series]

Categorical annotation of terminal states.

By default, all cells in transient cells will be labelled as NaN.

Return type: Optional[Series]

property terminal_states_probabilities: Optional[pandas.core.series.Series]

Aggregated probability of cells to be in terminal states.

Return type: Optional[Series]

to_adata(keep=('X', 'raw'), *, copy=True)

Serialize self to anndata.Anndata.

Parameters

keep (Union[Literal[‘all’], Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) –
Which attributes to keep from the underlying adata. Valid options are:
- ’all’ - keep all attributes specified in the signature.
- typing.Sequence - keep only subset of these attributes.
- dict - the keys correspond the attribute names and values to a subset of keys which to keep from this attribute. If the values are specified either as True or ‘all’, everything from this attribute will be kept.
copy (Union[bool, Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) – Whether to copy the data. Can be specified on per-attribute basis. Useful for attributes that store arrays. Attributes not specified here will not be copied.

Return type

AnnData

Returns

adata : anndata.AnnData Annotated data object.

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

Transition matrix of kernel.

Return type: Union[ndarray, spmatrix]

write(fname, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

CFLARE

class cellrank.tl.estimators.CFLARE(obj, obsp_key=None, **kwargs)[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[AnnData, ndarray, spmatrix, KernelExpression]) –
Can be one of the following:
- cellrank.tl.kernels.Kernel - kernel object.
- anndata.AnnData - annotated data object containing transition matrix in anndata.AnnData.obsp.
- numpy.ndarray - row-normalized sparse transition matrix.
- scipy.sparse.spmatrix - row-normalized sparse transition matrix.
obsp_key (Optional[str]) – Key in anndata.AnnData.obsp where the transition matrix is stored. Only used when obj is an anndata.AnnData object.

fit(k=20, **kwargs)[source]

Prepare self for terminal states prediction.

Parameters

k (int) – Number of eigenvectors to compute.
kwargs (Any) – Keyword arguments for compute_eigendecomposition().

Return type

TermStatesEstimator

Returns

Self and modifies the following field:

eigendecomposition - Eigendecomposition of transition_matrix.

predict(use=None, percentile=98, method='leiden', 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=None)[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, Sequence[int], None]) – Which or how many first eigenvectors to use as features for filtering and clustering. 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 (Literal[‘leiden’, ‘means’]) –
Method to be used for clustering. Valid option are:
- ’kmeans’ - sklearn.cluster.KMeans.
- ’leiden’ - scanpy.tl.leiden().
cluster_key (Optional[str]) – Key in anndata.AnnData.obs in order to associate names and colors with terminal_states.
n_clusters_kmeans (Optional[int]) – If None, this is set to use + 1.
n_neighbors (int) – Number of neighbors in a KNN graph. This is the \(K\) parameter for that, the number of neighbors for each cell. Only used when method = 'leiden'.
resolution (float) – Resolution parameter for scanpy.tl.leiden(). Should be chosen relatively small.
n_matches_min (int) – Filters out cells which don’t have at least n_matches_min neighbors from the same category. 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 anndata.AnnData.obsm as additional features for clustering. If None, use only the right eigenvectors.
n_comps (int) – Number of embedding components to be use when basis != None.
scale (Optional[bool]) – Scale the values to z-scores. If None, scale the values if basis != None.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

property absorption_probabilities: Optional[cellrank.tl._lineage.Lineage]

Absorption probabilities.

Informally, given a (finite, discrete) Markov chain with a set of transient states \(T\) and a set of absorbing states \(A\), the absorption probability for cell \(i\) from \(T\) to reach cell \(j\) from \(R\) is the probability that a random walk initialized in \(i\) will reach absorbing state \(j\).

In our context, states correspond to cells, in particular, absorbing states correspond to cells in terminal states.

Return type: Optional[Lineage]

property absorption_times: Optional[pandas.core.frame.DataFrame]

Mean and variance of the time until absorption.

Related to conditional mean first passage times. Corresponds to the expectation of the time until absorption, depending on initialization, and the variance.

Return type: Optional[DataFrame]

property adata: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData

property backward: bool

Direction of kernel.

Return type: bool

compute_absorption_probabilities(keys=None, 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.

For each cell, this computes the probability of being absorbed in any of the terminal_states. In particular, this corresponds to the probability that a random walk initialized in transient cell \(i\) will reach any cell from a fixed transient state before reaching a cell from any other transient state.

Parameters

keys (Optional[Sequence[str]]) – Terminal states for which to compute the absorption probabilities. If None, use all states defined in terminal_states.
solver (Union[str, Literal[‘direct’, ‘gmres’, ‘lgmres’, ‘bicgstab’, ‘gcrotmk’]]) –
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[Literal[‘all’], Sequence[Union[str, Sequence[str]]], Dict[Union[str, Sequence[str]], Literal[‘mean’, ‘var’]], 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 explicitly.

It might be beneficial to disable the progress bar as show_progress_bar = False because of many solves.
n_jobs (Optional[int]) – Number of parallel jobs to use when using an iterative solver.
backend (Literal[‘loky’, ‘multiprocessing’, ‘threading’]) – Which backend to use for multiprocessing. See joblib.Parallel for valid options.
show_progress_bar (bool) – Whether to show progress bar. Only used when solver != 'direct'.
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 valid options, see here. We recommend the ‘ilu’ preconditioner for badly conditioned problems.

Return type

Returns

Nothing, just updates the following fields:

absorption_probabilities - Absorption probabilities.
absorption_times - Mean and variance of the time until absorption. Only if time_to_absorption is specified.

compute_eigendecomposition(k=20, which='LR', alpha=1.0, 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 eigenvectors or eigenvalues to compute.
which (Literal[‘LR’, ‘LM’]) –
How to sort the eigenvalues. Valid option are:
- ’LR’ - the largest real part.
- ’LM’ - the 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) – Whether to compute only eigenvalues.
ncv (Optional[int]) – Number of Lanczos vectors generated.

Return type

Returns

Nothing, just updates the following field:

eigendecomposition - Eigendecomposition of transition_matrix.

compute_lineage_drivers(lineages=None, method=TestMethod.FISCHER, cluster_key=None, clusters=None, layer=None, use_raw=False, confidence_level=0.95, n_perms=1000, seed=None, **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]) – Lineage names from absorption_probabilities. If None, use all lineages.
method (Literal[‘fischer’, ‘perm_test’]) –
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 anndata.AnnData.obs to obtain cluster annotations. These are considered for clusters.
clusters (Union[str, Sequence, None]) – Restrict the correlations to these clusters.
layer (Optional[str]) – Key from anndata.AnnData.layers from which to get the expression. If None or ‘X’, use anndata.AnnData.X.
use_raw (bool) – Whether or not to use anndata.AnnData.raw to correlate gene expression.
confidence_level (float) – Confidence level for the confidence interval calculation. Must be in interval [0, 1].
n_perms (int) – Number of permutations to use when method = 'perm_test'.
seed (Optional[int]) – Random seed when method = 'perm_test'.
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

DataFrame

Returns

Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, one 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.

Also updates the following field:

lineage_drivers - the same pandas.DataFrame as described above.

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

Compute the degree of lineage priming.

It returns a score in [0, 1] 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'. If a dict, the key specifies a cluster key in anndata.AnnData.obs and the values specify cluster labels containing early cells.

Return type

Series

Returns

The priming degree.

Also updates the following field:

priming_degree - Priming degree.

compute_terminal_states(*args, **kwargs)

Compute terminal states of the process.

This is an alias for predict().

Parameters

args (Any) – Positional arguments.
kwargs (Any) – Keyword arguments arguments.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

copy(*, deep=False)

Return a copy of self.

Parameters: deep (bool) – Whether to return a deep copy or not. If True, this also copies the adata.
Return type: BaseEstimator
Returns: A copy of self.

property eigendecomposition: Optional[Dict[str, Any]]

Eigendecomposition of transition_matrix.

For non-symmetric real matrices, left and right eigenvectors will in general be different and complex. We compute both left and right eigenvectors.

Return type

Optional[Dict[str, Any]]

Returns

A dictionary with the following keys:

’D’ - the eigenvalues.
’eigengap’ - the eigengap.
’params’ - parameters used for the computation.
’V_l’ - left eigenvectors (optional).
’V_r’ - right eigenvectors (optional).
’stationary_dist’ - stationary distribution of transition_matrix, if present.

classmethod from_adata(adata, obsp_key)

Deserialize self from anndata.AnnData.

Parameters

adata (anndata.AnnData) – Annotated data object.
obsp_key (str) – Key in anndata.AnnData.obsp where the transition matrix is stored.

Return type

Returns

The deserialized object.

property kernel: cellrank.tl._mixins._kernel.KernelExpression

Underlying kernel expression.

Return type: ~KernelExpression

property lineage_drivers: Optional[pandas.core.frame.DataFrame]

Potential lineage drivers.

Computes Pearson correlation of each gene with fate probabilities for every terminal state. High Pearson correlation indicates potential lineage drivers. Also computes p-values and confidence intervals.

Return type

Optional[DataFrame]

Returns

Dataframe of shape (n_genes, n_lineages * 5) containing the following columns, one 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.

property params: Dict[str, Any]

Estimator parameters.

Return type: Dict[str, Any]

plot_absorption_probabilities(states=None, color=None, discrete=False, mode=PlotMode.EMBEDDING, time_key='latent_time', same_plot=True, title=None, cmap='viridis', **kwargs)

Plot continuous or categorical observations in an embedding or along pseudotime.

Parameters

states (Union[str, Sequence[str], None]) – States to plot.
color (Optional[str]) – Key in anndata.AnnData.obs.
discrete (bool) – Whether to plot the data as continuous or discrete observations. If the data cannot be plotted as continuous observations, it will be plotted as discrete.
mode (Literal[‘embedding’, ‘time’]) –
Valid options are:
- ’embedding’ - plot the embedding while coloring in continuous or categorical observations.
- ’time’ - plot the pseudotime on x-axis and the probabilities/memberships on y-axis.
time_key (str) – Key in anndata.AnnData.obs where pseudotime is stored. Only used when mode = 'time'.
title (Union[str, Sequence[str], None]) – Title of the plot(s).
same_plot (bool) – Whether to plot the data on the same plot or not. Only use when mode = 'embedding'. If True and discrete = False, color is ignored.
cmap (str) – Colormap for continuous data.
kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

Returns

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

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 access in anndata.AnnData.raw or not.
title_fmt (str) – Title format. Can include {gene}, {pval}, {qval} or {corr}, which will be substituted with the actual values.
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

Returns

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

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 anndata.AnnData.var or anndata.AnnData.varm, preferring for the former.
gene_sets (Optional[Dict[str, Sequence[str]]]) – Gene sets annotations of the form {‘gene_set_name’: [‘gene_1’, ‘gene_2’], …}.
gene_sets_colors (Optional[Sequence[str]]) – 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 anndata.AnnData.raw or not.
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

The axes object, if show = False. 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, marker='.', figsize=(5, 5), dpi=100, save=None, **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.
marker (str) – Marker symbol used, valid options can be found in matplotlib.markers.
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.
kwargs (Any) – Keyword arguments for matplotlib.pyplot.scatter().

Return type

Returns

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

plot_terminal_states(states=None, color=None, discrete=False, mode=PlotMode.EMBEDDING, time_key='latent_time', same_plot=True, title=None, cmap='viridis', **kwargs)

Plot continuous or categorical observations in an embedding or along pseudotime.

Parameters

states (Union[str, Sequence[str], None]) – States to plot.
color (Optional[str]) – Key in anndata.AnnData.obs.
discrete (bool) – Whether to plot the data as continuous or discrete observations. If the data cannot be plotted as continuous observations, it will be plotted as discrete.
mode (Literal[‘embedding’, ‘time’]) –
Valid options are:
- ’embedding’ - plot the embedding while coloring in continuous or categorical observations.
- ’time’ - plot the pseudotime on x-axis and the probabilities/memberships on y-axis.
time_key (str) – Key in anndata.AnnData.obs where pseudotime is stored. Only used when mode = 'time'.
title (Union[str, Sequence[str], None]) – Title of the plot(s).
same_plot (bool) – Whether to plot the data on the same plot or not. Only use when mode = 'embedding'. If True and discrete = False, color is ignored.
cmap (str) – Colormap for continuous data.
kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type

Returns

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

property priming_degree: Optional[pandas.core.series.Series]

Priming degree.

Given a cell \(i\) and a set of terminal states, this quantifies how committed vs. naive cell \(i\) is, i.e. its degree of pluripotency. Low values correspond to naive cells (high degree of pluripotency), high values correspond to committed cells (low degree of pluripotency).

Return type: Optional[Series]

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

rename_terminal_states(new_names)

Rename categories in terminal_states.

Parameters

new_names (Mapping[str, str]) – Mapping where keys corresponds to the old names and the values to the new names. The new names must be unique.

Return type

Returns

Nothing, just updates the names of:

terminal_states - Categorical annotation of terminal states.

set_terminal_states(labels, cluster_key=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 a 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.AnnData.obs_names. If only 1 key is provided, values should correspond to terminal state clusters if a categorical pandas.Series can be found in anndata.AnnData.obs.
cluster_key (Optional[str]) – Key in anndata.AnnData.obs in order to associate names and colors with terminal_states. Each terminal state will be given the name and color corresponding to the cluster it mostly overlaps with.
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.

Return type

Returns

Nothing, just updates the following fields:

terminal_states - Categorical annotation of terminal states.
terminal_states_probabilities - Aggregated probability of cells to be in terminal states.

property shape: Tuple[int, int]

Shape of the kernel.

Return type: Tuple[int, int]

property terminal_states: Optional[pandas.core.series.Series]

Categorical annotation of terminal states.

By default, all cells in transient cells will be labelled as NaN.

Return type: Optional[Series]

property terminal_states_probabilities: Optional[pandas.core.series.Series]

Aggregated probability of cells to be in terminal states.

Return type: Optional[Series]

to_adata(keep=('X', 'raw'), *, copy=True)

Serialize self to anndata.Anndata.

Parameters

keep (Union[Literal[‘all’], Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) –
Which attributes to keep from the underlying adata. Valid options are:
- ’all’ - keep all attributes specified in the signature.
- typing.Sequence - keep only subset of these attributes.
- dict - the keys correspond the attribute names and values to a subset of keys which to keep from this attribute. If the values are specified either as True or ‘all’, everything from this attribute will be kept.
copy (Union[bool, Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) – Whether to copy the data. Can be specified on per-attribute basis. Useful for attributes that store arrays. Attributes not specified here will not be copied.

Return type

AnnData

Returns

adata : anndata.AnnData Annotated data object.

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

Transition matrix of kernel.

Return type: Union[ndarray, spmatrix]

write(fname, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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 anndata.AnnData.layers where velocities are stored.
xkey (str) – Key in anndata.AnnData.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 anndata.AnnData.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=VelocityMode.DETERMINISTIC, backward_mode=BackwardMode.TRANSPOSE, scheme=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 (Literal[‘deterministic’, ‘stochastic’, ‘sampling’, ‘monte_carlo’]) –
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 (Literal[‘transpose’, ‘negate’]) –
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 counter everything tending to orthogonality in high dimensions.
scheme (Union[Literal[‘dot_product’, ‘cosine’, ‘correlation’], Callable]) –
Similarity scheme between cells as described in [Li et al., 2021]. Can be one of the following:
- ’dot_product’ - cellrank.tl.kernels.DotProductScheme.
- ’cosine’ - cellrank.tl.kernels.CosineScheme.
- ’correlation’ - cellrank.tl.kernels.CorrelationScheme.
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.

Return type

VelocityKernel

Returns

Self and updates the following fields:

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.

Return type

Returns

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

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.

Return type

Returns

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

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.

Return type

Returns

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

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.

Return type

Returns

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

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.

Return type

Returns

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

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.

Return type

Returns

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

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:

transcriptomic similarities, computed using e.g. scanpy.pp.neighbors(), see [Wolf et al., 2018].

spatial similarities, computed using e.g. squidpy.gr.spatial_neighbors(), see [Palla et al., 2021].

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.
Return type: ConnectivityKernel
Returns: Self and updated transition_matrix.

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].

Parameters

threshold_scheme (Union[Literal[‘soft’, ‘hard’], Callable]) –
Which method to use when biasing the graph. Valid options are:
- ’hard’ - based on 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.
- ’soft’ - based on 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.
- callable - any function conforming to the signature of cellrank.tl.kernels.ThresholdSchemeABC.__call__().
frac_to_keep (float) – The frac_to_keep * number of the 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'. 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 (Literal[‘loky’, ‘multiprocessing’, ‘threading’]) – Which backend to use for parallelization. See joblib.Parallel for valid options.
kwargs (Any) – Keyword arguments for threshold_scheme.

Return type

PseudotimeKernel

Returns

Self and updated transition_matrix.

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

Return type

Returns

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 pseudotime 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.

Return type

Returns

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

CytoTRACE Kernel

class cellrank.tl.kernels.CytoTRACEKernel(adata, backward=False, layer='Ms', aggregation=CytoTRACEAggregation.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.
- ’hmean’ - harmonic mean.
- ’gmean’ - geometric 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=CytoTRACEAggregation.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.
- ’hmean’ - harmonic mean.
- ’gmean’ - geometric 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

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].

Parameters

threshold_scheme (Union[Literal[‘soft’, ‘hard’], Callable]) –
Which method to use when biasing the graph. Valid options are:
- ’hard’ - based on 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.
- ’soft’ - based on 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.
- callable - any function conforming to the signature of cellrank.tl.kernels.ThresholdSchemeABC.__call__().
frac_to_keep (float) – The frac_to_keep * number of the 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'. 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 (Literal[‘loky’, ‘multiprocessing’, ‘threading’]) – Which backend to use for parallelization. See joblib.Parallel for valid options.
kwargs (Any) – Keyword arguments for threshold_scheme.

Return type

PseudotimeKernel

Returns

Self and updated transition_matrix.

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 anndata.AnnData.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 (Literal[‘normal’, ‘binomial’, ‘poisson’, ‘gamma’, ‘gaussian’, ‘inv_gauss’]) – Name of the distribution. Available distributions can be found here.
link (Literal[‘identity’, ‘logit’, ‘inverse’, ‘log’, ‘inverse-squared’]) – 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[str, Any], 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[str, Any]) – Keyword arguments for pygam.s.
kwargs (Any) – 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.

Return type

GAM

Returns

Fits the model and returns self.

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.

Return type

Returns

Updates and returns the following field:

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

property adata: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData
Returns: adata : anndata.AnnData Annotated data object.

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

Also update the following fields:

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.

property model: Any

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.

Return type

Optional[Figure]

Returns

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

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 anndata.AnnData.var_names.
lineage (Optional[str]) – Name of a lineage in anndata.AnnData.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 (Optional[str]) – Key in anndata.AnnData.layers or ‘X’ for anndata.AnnData.X. If use_raw = True, it’s always set to ‘X’.
time_key (str) – Key in anndata.AnnData.obs where the pseudotime is stored.
use_raw (bool) – Whether to access anndata.AnnData.raw.
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.

Return type

Returns

Nothing, just 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.

property prepared: Whether the model is prepared for fitting.

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int]

Number of cells in adata.

Return type: Tuple[int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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.

Return type

SKLearnModel

Returns

Fits the model and returns self.

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.

Return type

Returns

Updates and returns the following field:

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

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

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: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData
Returns: adata : anndata.AnnData Annotated data object.

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

Also update the following fields:

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.

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.

Return type

Optional[Figure]

Returns

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

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 anndata.AnnData.var_names.
lineage (Optional[str]) – Name of a lineage in anndata.AnnData.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 (Optional[str]) – Key in anndata.AnnData.layers or ‘X’ for anndata.AnnData.X. If use_raw = True, it’s always set to ‘X’.
time_key (str) – Key in anndata.AnnData.obs where the pseudotime is stored.
use_raw (bool) – Whether to access anndata.AnnData.raw.
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.

Return type

Returns

Nothing, just 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.

property prepared: Whether the model is prepared for fitting.

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int]

Number of cells in adata.

Return type: Tuple[int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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=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 (Literal[‘auto’, ‘density’]) –
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[ndarray, Literal[‘default’], 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 anndata.AnnData.var_names.
lineage – Name of a lineage in anndata.AnnData.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 anndata.AnnData.layers or ‘X’ for anndata.AnnData.X. If use_raw = True, it’s always set to ‘X’.
time_key – Key in anndata.AnnData.obs where the pseudotime is stored.
use_raw – Whether to access anndata.AnnData.raw.
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.

Return type

GAMR

Returns

Nothing, just 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.

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.

Return type

GAMR

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.

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].

Return type

Returns

Updates and returns the following field:

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

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().
level (float) – Confidence level.

Return type

Returns

Updates and returns the following field:

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

copy()[source]

Return a copy of self.

Return type: GAMR

property adata: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData
Returns: adata : anndata.AnnData Annotated data object.

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

Also update the following fields:

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.

property model: Any

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.

Return type

Optional[Figure]

Returns

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

property prepared: Whether the model is prepared for fitting.

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int]

Number of cells in adata.

Return type: Tuple[int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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, obsp_key=None)[source]

Base class for all estimators.

Parameters

obj (Union[AnnData, ndarray, spmatrix, KernelExpression]) –
Can be one of the following:
- cellrank.tl.kernels.Kernel - kernel object.
- anndata.AnnData - annotated data object containing transition matrix in anndata.AnnData.obsp.
- numpy.ndarray - row-normalized sparse transition matrix.
- scipy.sparse.spmatrix - row-normalized sparse transition matrix.
obsp_key (Optional[str]) – Key in anndata.AnnData.obsp where the transition matrix is stored. Only used when obj is an anndata.AnnData object.

to_adata(keep=('X', 'raw'), *, copy=True)[source]

Serialize self to anndata.Anndata.

Parameters

keep (Union[Literal[‘all’], Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) –
Which attributes to keep from the underlying adata. Valid options are:
- ’all’ - keep all attributes specified in the signature.
- typing.Sequence - keep only subset of these attributes.
- dict - the keys correspond the attribute names and values to a subset of keys which to keep from this attribute. If the values are specified either as True or ‘all’, everything from this attribute will be kept.
copy (Union[bool, Sequence[Literal[‘X’, ‘raw’, ‘layers’, ‘obs’, ‘var’, ‘obsm’, ‘varm’, ‘obsp’, ‘varp’, ‘uns’]]]) – Whether to copy the data. Can be specified on per-attribute basis. Useful for attributes that store arrays. Attributes not specified here will not be copied.

Return type

AnnData

Returns

adata : anndata.AnnData Annotated data object.

classmethod from_adata(adata, obsp_key)[source]

Deserialize self from anndata.AnnData.

Parameters

adata (anndata.AnnData) – Annotated data object.
obsp_key (str) – Key in anndata.AnnData.obsp where the transition matrix is stored.

Return type

Returns

The deserialized object.

copy(*, deep=False)[source]

Return a copy of self.

Parameters: deep (bool) – Whether to return a deep copy or not. If True, this also copies the adata.
Return type: BaseEstimator
Returns: A copy of self.

property params: Dict[str, Any]

Estimator parameters.

Return type: Dict[str, Any]

abstract fit(*args, **kwargs)[source]

Fit an estimator.

Parameters

args (Any) – Positional arguments.
kwargs (Any) – Keyword arguments.

Return type

Returns

Self.

abstract predict(*args, **kwargs)[source]

Run a prediction.

Parameters

args (Any) – Positional arguments.
kwargs (Any) – Keyword arguments.

Return type

Returns

Nothing.

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.

Return type: AnnData
Returns: anndata.AnnData Annotated data object.

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 anndata.AnnData.obsm for which to compute the projection.
key_added (Optional[str]) – If not None and copy = False, save the result to anndata.AnnData.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.

Return type

KernelExpression

Returns

cellrank.tl.kernels.KernelExpression Self.

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], Tuple[float, float]]], None]) –
Cells from which to sample the starting points. If None, use all cells. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'dpt_pseudotime': [0, 0.1]} means that starting points for random walks will be sampled uniformly from cells whose pseudotime is in [0, 0.1].
stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str], Tuple[float, float]]], None]) –
Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'clusters': ['Alpha', 'Beta']} and successive_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

Returns

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 flow.
cluster_key (str) – Key in anndata.AnnData.obs where clustering is stored.
time_key (str) – Key in anndata.AnnData.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

The axes object, if show = False. 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, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int, int]

(n_cells, n_cells).

Return type: Tuple[int, int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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, determine the key automatically.

Return type

Returns

None Updates the adata with the following fields:

.obsp['{key}'] - the transition matrix.

.uns['{key}_params'] - parameters used for calculation.

ExperimentalTime Kernel

class cellrank.tl.kernels.ExperimentalTimeKernel(adata, backward=False, time_key='exp_time', compute_cond_num=False, **kwargs)[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 anndata.AnnData.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 flow.
cluster_key (str) – Key in anndata.AnnData.obs where clustering is stored.
time_key (Optional[str]) – Key in anndata.AnnData.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

Returns

The axes object, if show = False. 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.

Return type: AnnData
Returns: anndata.AnnData Annotated data object.

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 anndata.AnnData.obsm for which to compute the projection.
key_added (Optional[str]) – If not None and copy = False, save the result to anndata.AnnData.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.

Return type

KernelExpression

Returns

cellrank.tl.kernels.KernelExpression Self.

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], Tuple[float, float]]], None]) –
Cells from which to sample the starting points. If None, use all cells. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'dpt_pseudotime': [0, 0.1]} means that starting points for random walks will be sampled uniformly from cells whose pseudotime is in [0, 0.1].
stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str], Tuple[float, float]]], None]) –
Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'clusters': ['Alpha', 'Beta']} and successive_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

Returns

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, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int, int]

(n_cells, n_cells).

Return type: Tuple[int, int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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, determine the key automatically.

Return type

Returns

None Updates the adata with the following fields:

.obsp['{key}'] - the transition matrix.

.uns['{key}_params'] - parameters used for calculation.

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.

compute_transition_matrix(threshold='auto', last_time_point=LastTimePoint.DIAGONAL, conn_kwargs=mappingproxy({}), **kwargs)[source]

Compute transition matrix using transport maps.

Parameters

threshold (Union[float, Literal[‘auto’], None]) –
How to remove small non-zero values from the transition matrix. Valid options are:
- ’auto’ - find the maximum threshold value which will not remove every non-zero value from any row.
- float - value in [0, 100] corresponding to a percentage of non-zeros to remove. Rows where all values are removed will have uniform distribution.
- None - do not threshold.
last_time_point (LastTimePoint) –
How to define transitions within the last time point. Valid options are:
- {ltp.UNIFORM!r} - row-normalized matrix of 1s for transitions within the last time point.
- {ltp.DIAGONAL!r} - diagonal matrix with 1s on the diagonal.
- {ltp.CONNECTIVITIES!r} - use transitions from cellrank.tl.kernels.ConnectivityKernel derived from the last time point subset of adata.
conn_kwargs (Mapping[str, Any]) – Keyword arguments for scanpy.pp.neighbors() when using last_time_point = {ltp.CONNECTIVITIES!r}. Can have ‘density_normalize’ for cellrank.tl.kernels.ConnectivityKernel.compute_transition_matrix().

Return type

KernelExpression

Returns

Self and updated transition_matrix.

property transport_maps: Optional[Dict[Tuple[Any, Any], anndata._core.anndata.AnnData]]

Transport maps for consecutive time pairs.

Return type: Optional[Dict[Tuple[Any, Any], AnnData]]

property adata: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData
Returns: anndata.AnnData Annotated data object.

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 anndata.AnnData.obsm for which to compute the projection.
key_added (Optional[str]) – If not None and copy = False, save the result to anndata.AnnData.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.

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], Tuple[float, float]]], None]) –
Cells from which to sample the starting points. If None, use all cells. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'dpt_pseudotime': [0, 0.1]} means that starting points for random walks will be sampled uniformly from cells whose pseudotime is in [0, 0.1].
stop_ixs (Union[Sequence[str], Dict[str, Union[str, Sequence[str], Tuple[float, float]]], None]) –
Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as:
- dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.
- typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.
For example {'clusters': ['Alpha', 'Beta']} and successive_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

Returns

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 flow.
cluster_key (str) – Key in anndata.AnnData.obs where clustering is stored.
time_key (Optional[str]) – Key in anndata.AnnData.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

Returns

The axes object, if show = False. Nothing, just plots the figure. Optionally saves it based on save.

static read(fname, adata=None, copy=False)

Deserialize self from a file.

Parameters

fname (Union[str, Path]) – Filename from which to read the object.
adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.
copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type

IOMixin

Returns

The deserialized object.

property shape: Tuple[int, int]

(n_cells, n_cells).

Return type: Tuple[int, int]

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, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters

fname (Union[str, Path]) – Filename where to save the object.
write_adata (bool) – Whether to save adata object or not, if present.
ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type

Returns

Nothing, just writes itself to a file using pickle.

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, determine the key automatically.

Return type

Returns

None Updates the adata with the following fields:

.obsp['{key}'] - the transition matrix.

.uns['{key}_params'] - parameters used for calculation.

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.

Return type

Returns

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

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

Return type

Returns

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.

Return type

csr_matrix

Returns

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: anndata._core.anndata.AnnData

Annotated data object.

Return type: AnnData
Returns: adata : anndata.AnnData Annotated data object.

property shape: Tuple[int]

Number of cells in adata.

Return type: Tuple[int]

property model: Any

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 anndata.AnnData.var_names.
lineage (Optional[str]) – Name of a lineage in anndata.AnnData.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 (Optional[str]) – Key in anndata.AnnData.layers or ‘X’ for anndata.AnnData.X. If use_raw = True, it’s always set to ‘X’.
time_key (str) – Key in anndata.AnnData.obs where the pseudotime is stored.
use_raw (bool) – Whether to access anndata.AnnData.raw.
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.

Return type

Returns

Nothing, just 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.

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.

Return type

Returns

Fits the model and returns self.

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.

Return type

Returns

Updates and returns the following field:

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

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type

Returns

Updates and returns the following field:

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

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

x_test (Optional[ndarray]) – Array of shape (n_samples,) used for confidence interval calculation. If None, use x_test.
kwargs – Keyword arguments for underlying model’s confidence method or for default_confidence_interval().

Return type