mojolearn.FactorAnalysis

class mojolearn.FactorAnalysis(n_components=None, *, tol=0.01, copy=True, max_iter=1000, noise_variance_init=None, svd_method='randomized', iterated_power=3, rotation=None, random_state=0, numeric_mode=None)

Bases: _Base

Factor analysis: a linear Gaussian latent variable model.

Follows scikit-learn’s FactorAnalysis, fitted by EM. Both svd_method values use an exact SVD at every iteration (scikit-learn’s "randomized" is an approximation of it), so iterated_power and random_state have no effect.

Parameters:

• n_components (int or None, default None) – Dimension of the latent space; None uses n_features.

• tol (float, default 1e-2) – Stop when the log-likelihood gain falls below this.

• copy (bool, default True) – Accepted for scikit-learn compatibility; X is never modified.

• max_iter (int, default 1000) – Maximum number of EM iterations.

• noise_variance_init (array-like of shape (n_features,) or None, default None) – Starting noise variances; None uses ones.

• svd_method ({“lapack”, “randomized”}, default “randomized”) – Accepted for scikit-learn compatibility; both run the exact SVD.

• iterated_power (int, default 3) – Accepted for scikit-learn compatibility; unused.

• rotation ({“varimax”, “quartimax”} or None, default None) – Rotation applied to the fitted components.

• random_state (int or None, default 0) – Accepted for scikit-learn compatibility; unused.

• numeric_mode ({“identical”, “fast”} or None, default None) – Numeric mode for this estimator. None uses the package default ("identical" unless changed). "identical" gives the same bits on NVIDIA and AMD GPUs; "fast" applies on Apple GPUs.

Variables:

• components_ (ndarray of shape (n_components, n_features)) – Factor loadings.

• noise_variance_ (ndarray of shape (n_features,))

• mean_ (ndarray of shape (n_features,))

• loglike_ (list of float) – Log-likelihood at each iteration.

• n_iter_ (int)

• n_features_in_ (int)

Raises:

ValueError – For an unsupported svd_method or rotation, or a noise_variance_init of the wrong length.

Examples

>>> import numpy as np, mojolearn
>>> X = np.random.default_rng(0).random((1000, 8), dtype=np.float32)
>>> fa = mojolearn.FactorAnalysis(n_components=2).fit(X)
>>> Z = fa.transform(X)

__init__(n_components=None, *, tol=0.01, copy=True, max_iter=1000, noise_variance_init=None, svd_method='randomized', iterated_power=3, rotation=None, random_state=0, numeric_mode=None)

Methods

fit(X[, y])	Fit the model with EM.
fit_transform(X[, y])	Fit to X, then return transform(X).
get_covariance()	Return the model covariance components_.T @ components_ + diag(noise_variance_).
get_params([deep])	Return this estimator's constructor parameters.
get_precision()	Return the inverse of the model covariance.
score(X[, y])	Return the average log-likelihood of the samples.
score_samples(X)	Return the log-likelihood of each sample under the model.
set_params(**params)	Set constructor parameters by keyword.
transform(X)	Return the expected latent variables for each sample.

fit(X, y=None)

Fit the model with EM.

Parameters:

• X (array-like of shape (n_samples, n_features))

• y (ignored)

Returns:

self

transform(X)

Return the expected latent variables for each sample.

Parameters:

X (array-like of shape (n_samples, n_features))

Returns:

ndarray of shape (n_samples, n_components), float32

get_covariance()

Return the model covariance components_.T @ components_ + diag(noise_variance_).

Returns:

ndarray of shape (n_features, n_features), float32

get_precision()

Return the inverse of the model covariance.

Returns:

ndarray of shape (n_features, n_features), float32

Raises:

ValueError – If the covariance is singular.

score_samples(X)

Return the log-likelihood of each sample under the model.

Parameters:

X (array-like of shape (n_samples, n_features))

Returns:

ndarray of shape (n_samples,), float32

score(X, y=None)

Return the average log-likelihood of the samples.

Parameters:

• X (array-like of shape (n_samples, n_features))

• y (ignored)

Returns:

float