observation.posteriors#

Posterior distributions for observation model parameters.

Classes

`LoadingPosterior`	Posterior distribution over loading matrices.
`ARDPosterior`	Posterior distribution over ARD parameters.
`ObsMeanPosterior`	Posterior distribution over observation mean parameters.
`ObsPrecPosterior`	Posterior distribution over observation precision parameters.
`ObsParamsPosterior`	Posterior distributions over all observation model parameters.

class LoadingPosterior( mean: ndarray | None = None, cov: ndarray | None = None, moment: ndarray | None = None, )[source]#

Posterior distribution over loading matrices.

Parameters:

meanndarray of float, shape (y_dim, x_dim) or None, default None: Posterior mean.
covndarray of float, shape (y_dim, x_dim, x_dim) or None, default None: Posterior covariances.
momentndarray of float, shape (y_dim, x_dim, x_dim) or None, default None: Posterior second moments.

Attributes:

meanndarray of float, shape (y_dim, x_dim) or None: Posterior mean.
covndarray of float, shape (y_dim, x_dim, x_dim) or None: Posterior covariances.
momentndarray of float, shape (y_dim, x_dim, x_dim) or None: Posterior second moments.

get_groups( y_dims: ndarray, ) → tuple[list[ndarray], list[ndarray], list[ndarray]][source]#

Get list of views into posterior parameters, one per group.

Parameters:

y_dimsndarray of int, shape (n_groups,): Dimensionalities of each observed group.

Returns:

group_meanslist of ndarray or None: List of views into mean, one per group. None if mean is None.
group_covslist of ndarray or None: List of views into cov, one per group. None if cov is None.
group_momentslist of ndarray or None: List of views into moment, one per group. None if moment is None.

compute_moment(in_place: bool = True) → ndarray[source]#

Compute posterior second moments E[C_i C_i^T] for each row i.

Parameters:

in_placebool, default True: If True, store in self.moment and return reference. If False, return new array.

Returns:

ndarray: Second moments, shape (y_dim, x_dim, x_dim).

compute_squared_norms(y_dims: ndarray) → ndarray[source]#

Compute expected squared norm of each column per group.

Parameters:

y_dimsndarray of int, shape (n_groups,): Dimensionalities of each observed group.

Returns:

ndarray: Squared norms, shape (n_groups, x_dim).

get_subset_dims( x_indices: ndarray, in_place: bool = True, ) → Self[source]#

Keep only specified latent dimensions.

Parameters:

x_indicesndarray of int: Indices of latent dimensions to keep.
in_placebool, default True: If True, modify self. If False, return new instance.

Returns:

Self: Modified or new instance.

class ARDPosterior( a: ndarray | None = None, b: ndarray | None = None, mean: ndarray | None = None, )[source]#

Posterior distribution over ARD parameters.

Parameters:

andarray of float, shape (n_groups,) or None, default None: Shape parameters.
bndarray of float, shape (n_groups, x_dim) or None, default None: Rate parameters.
meanndarray of float, shape (n_groups, x_dim) or None, default None: Posterior mean a/b.

Attributes:

andarray of float, shape (n_groups,) or None: Shape parameters.
bndarray of float, shape (n_groups, x_dim) or None: Rate parameters.
meanndarray of float, shape (n_groups, x_dim) or None: Posterior mean a/b.

compute_mean(in_place: bool = True) → ndarray[source]#

Compute posterior mean a/b.

Parameters:

in_placebool, default True: If True, store in self.mean and return reference. If False, return new array.

Returns:

ndarray: Posterior mean, shape (n_groups, x_dim).

get_subset_dims( x_indices: ndarray, in_place: bool = True, ) → Self[source]#

Keep only specified latent dimensions.

Parameters:

x_indicesndarray of int: Indices of latent dimensions to keep.
in_placebool, default True: If True, modify self. If False, return new instance.

Returns:

Self: Modified or new instance.

class ObsMeanPosterior( mean: ndarray | None = None, cov: ndarray | None = None, )[source]#

Posterior distribution over observation mean parameters.

Parameters:

meanndarray of float, shape (y_dim,) or None, default None: Posterior mean.
covndarray of float, shape (y_dim,) or None, default None: Posterior variance (diagonal).

Attributes:

meanndarray of float, shape (y_dim,) or None: Posterior mean.
covndarray of float, shape (y_dim,) or None: Posterior variance (diagonal).

get_groups( y_dims: ndarray, ) → tuple[list[ndarray], list[ndarray]][source]#

Get list of views into posterior parameters, one per group.

Parameters:

y_dimsndarray of int, shape (n_groups,): Dimensionalities of each observed group.

Returns:

group_meanslist of ndarray or None: List of views into mean, one per group. None if mean is None.
group_covslist of ndarray or None: List of views into cov, one per group. None if cov is None.

class ObsPrecPosterior( a: float | None = None, b: ndarray | None = None, mean: ndarray | None = None, )[source]#

Posterior distribution over observation precision parameters.

Parameters:

afloat or None, default None: Shape parameter (scalar, shared across dimensions).
bndarray of float, shape (y_dim,) or None, default None: Rate parameters.
meanndarray of float, shape (y_dim,) or None, default None: Posterior mean a/b.

Attributes:

afloat or None: Shape parameter (scalar, shared across dimensions).
bndarray of float, shape (y_dim,) or None: Rate parameters.
meanndarray of float, shape (y_dim,) or None: Posterior mean a/b.

get_groups( y_dims: ndarray, ) → tuple[list[ndarray], list[ndarray]][source]#

Get list of views into posterior parameters, one per group.

Parameters:

y_dimsndarray of int, shape (n_groups,): Dimensionalities of each observed group.

Returns:

group_meanslist of ndarray or None: List of views into mean, one per group. None if mean is None.
group_bslist of ndarray or None: List of views into b, one per group. None if b is None.

compute_mean(in_place: bool = True) → ndarray[source]#

Compute posterior mean a/b.

Parameters:

in_placebool, default True: If True, store in self.mean and return reference. If False, return new array.

Returns:

ndarray: Posterior mean, shape (y_dim,).

Posterior distributions over all observation model parameters.

Bundle of posteriors q(C), q(alpha), q(d), q(phi) with methods for sampling, computing point estimates, and analysis.

Parameters:

x_dimint or None, default None: Number of latent dimensions.
y_dimsndarray of int, shape (n_groups,) or None, default None: Dimensionalities of each observed group.
CLoadingPosterior or None, default None: Posterior over loading matrices.
alphaARDPosterior or None, default None: Posterior over ARD parameters.
dObsMeanPosterior or None, default None: Posterior over observation means.
phiObsPrecPosterior or None, default None: Posterior over observation precisions.

Attributes:

x_dimint or None: Number of latent dimensions.
y_dimsndarray of int, shape (n_groups,) or None: Dimensionalities of each observed group.
CLoadingPosterior: Posterior over loading matrices.
alphaARDPosterior: Posterior over ARD parameters.
dObsMeanPosterior: Posterior over observation means.
phiObsPrecPosterior: Posterior over observation precisions.

Examples

After fitting a GFA model, access the observation posterior:

>>> model = GFAModel()
>>> model.fit(Y)
>>> obs_post = model.obs_posterior

Get posterior mean as a realization:

>>> params = obs_post.posterior_mean
>>> params.C.shape
(20, 5)

Sample from the posterior:

>>> rng = np.random.default_rng(42)
>>> sample = obs_post.sample(rng)

property posterior_mean: ObsParamsRealization#

Return posterior means as a realization.

Returns:

ObsParamsRealization: Realization with posterior mean values.

sample( rng: Generator, ) → ObsParamsRealization[source]#

Draw a sample from the posterior distributions.

Samples from q(C), q(alpha), q(d), q(phi) independently.

Parameters:

rngnumpy.random.Generator: Random number generator.

Returns:

ObsParamsRealization: Sampled parameter values.

is_initialized() → bool[source]#

Check if all posterior parameters have been initialized.

Returns:

bool: True if all required arrays are non-None.

get_subset_dims( x_indices: ndarray, in_place: bool = True, ) → Self[source]#

Keep only specified latent dimensions.

Parameters:

x_indicesndarray of int: Indices of latent dimensions to keep.
in_placebool, default True: If True, modify self. If False, return new instance.

Returns:

Self: Modified or new instance.

copy() → Self[source]#

Return a deep copy.

Returns:

Self: Deep copy of this instance.

compute_snr( y_dims: ndarray | None = None, ) → ndarray[source]#

Compute signal-to-noise ratio for each group.

Parameters:

y_dimsndarray or None, default None: Dimensionalities of observed groups. If None, uses self.y_dims.

Returns:

ndarray: SNR for each group, shape (n_groups,).

static get_dim_types(n_groups: int) → ndarray[source]#

Generate all dimension types for n_groups.

Parameters:

n_groupsint: Number of observed groups.

Returns:

ndarray: Boolean array, shape (n_groups, 2^n_groups). Column j indicates which groups are involved in dimension type j.

compute_dimensionalities( cutoff_shared_var: float = 0.02, cutoff_snr: float = 0.001, ) → tuple[ndarray, ndarray, ndarray, ndarray][source]#

Compute dimensionalities and variance explained by dimension type.

Parameters:

cutoff_shared_varfloat, default 0.02: Minimum fraction of shared variance for significance.
cutoff_snrfloat, default 0.001: Minimum SNR for any latents to be significant.

Returns:

num_dimndarray of int, shape (n_dim_types,): Number of each dimension type.
sig_dimsndarray of bool, shape (n_groups, x_dim): Significant dimensions.
var_expndarray of float, shape (n_groups, n_dim_types): Variance explained by type.
dim_typesndarray of bool, shape (n_groups, n_dim_types): Dimension type indicators.

static compute_dims_pairs( num_dim: ndarray, dim_types: ndarray, var_exp: ndarray, ) → tuple[ndarray, ndarray, ndarray][source]#

Analyze shared dimensionalities between pairs of groups.

Parameters:

num_dimndarray: Number of each dimension type, shape (n_dim_types,).
dim_typesndarray: Dimension type indicators, shape (n_groups, n_dim_types).
var_expndarray: Variance explained by type, shape (n_groups, n_dim_types).

Returns:

pair_dimsndarray of int, shape (n_pairs, 3): Dimensionalities per pair.
pair_var_expndarray of float, shape (n_pairs, 2): Variance explained per pair.
pairsndarray of int, shape (n_pairs, 2): Pair indices.