smm package

Submodules

smm.example module

smm.smm module

Module contents

t-Student Mixture Models Module (smm).

• This module allows you to model data by a mixture of t-Student distributions, estimating the parameters with Expectation-Maximisation. It is an implementation of the paper: ‘Robust mixture modelling using the t distribution’, D. Peel and G. J. McLachlan. Published at: Statistics and Computing (2000) 10, 339-348.
• This module has reused code and comments from sklearn.mixture.gmm.

class smm.SMM(n_components=1, covariance_type='full', random_state=None, tol=1e-06, min_covar=1e-06, n_iter=1000, n_init=1, params='wmcd', init_params='wmcd')

Bases: sklearn.base.BaseEstimator

t-Student Mixture Model SMM class.

Representation of a t-Student mixture model probability distribution. This class allows for easy evaluation of, sampling from, and maximum-likelihood estimation of the parameters of an SMM distribution.

Initializes parameters such that every mixture component has zero mean and identity covariance.

Parameters:

• n_components (int, optional.) – Number of mixture components. Defaults to 1.

• covariance_type (string, optional.) – String describing the type of covariance parameters to use. Must be one of ‘spherical’, ‘tied’, ‘diag’, ‘full’. Defaults to ‘full’.

• random_state (RandomState or an int seed.) – A random number generator instance. None by default.

• tol (float, optional.) – Convergence threshold. EM iterations will stop when average gain in log-likelihood is below this threshold. Defaults to 1e-6.

• min_covar (float, optional.) – Floor on the diagonal of the covariance matrix to prevent overfitting. Defaults to 1e-6.

• n_iter (int, optional.) – Number of EM iterations to perform. Defaults to 1000.

• n_init (int, optional.) –

  Number of initializations to perform. The best result

  is kept.

  Defaults to 1.

• params (string, optional.) – Controls which parameters are updated in the training process. Can contain any combination of ‘w’ for weights, ‘m’ for means, ‘c’ for covars, and ‘d’ for the degrees of freedom. Defaults to ‘wmcd’.

• init_params (string, optional.) – Controls which parameters are updated in the initialization process. Can contain any combination of ‘w’ for weights, ‘m’ for means, ‘c’ for covars, and ‘d’ for the degrees of freedom. Defaults to ‘wmcd’.

Variables:

• weights (array, shape (n_components,).) – This attribute stores the mixing weights for each mixture component.
• means (array_like, shape (n_components, n_features).) – Mean parameters for each mixture component.
• covars (array_like.) –

  Covariance parameters for each mixture component. The shape depends on covariance_type:

  (n_components, n_features) if ‘spherical’, (n_features, n_features) if ‘tied’, (n_components, n_features) if ‘diag’, (n_components, n_features, n_features) if ‘full’

• converged (bool.) – True when convergence was reached in fit(), False otherwise.

aic(X)

Akaike information criterion for the current model fit and the proposed data.

Parameters:X (array_like, shape (n_samples, n_features).) Returns: Return type:A float (the lower the better)

bic(X)

Bayesian information criterion for the current model fit and the proposed data.

Parameters:X (array_like, shape (n_samples, n_features).) Returns: Return type:A float (the lower the better)

covariances

Covariance parameters for each mixture component.

Returns:

• The covariance matrices for all the classes.
• The shape depends on the type of covariance matrix – (n_classes, n_features) if ‘diag’, (n_classes, n_features, n_features) if ‘full’ (n_classes, n_features) if ‘spherical’, (n_features, n_features) if ‘tied’,

degrees

Returns the degrees of freedom of each component in the mixture.

static dist_covar_to_match_cov_type(tied_cv, covariance_type, n_components)

Create all the covariance matrices from a given template.

Parameters:

• tied_cv (array_like, shape (n_features, n_features).) – Tied covariance that is going to be converted to other type.
• covariance_type (string.) – Type of the covariance parameters. Must be one of ‘spherical’, ‘tied’, ‘diag’, ‘full’.
• n_components (integer value.) – Number of components in the mixture.

Returns:

cv – parameter). Tied covariance in the format specified by the user.

Return type:

array_like, shape (depends on the covariance_type

fit(X, y=None)

Estimate model parameters with the EM algorithm.

A initialization step is performed before entering the em algorithm. If you want to avoid this step, set the keyword argument init_params to the empty string ‘’ when creating the SMM object. Likewise, if you would like just to do an initialization, set n_iter=0.

Parameters:

• X (array_like, shape (n_samples, n_features).)
• y (not used, just for compatibility with sklearn API.)

means

Returns the means of each component in the mixture.

static multivariate_t_rvs(m, S, df=inf, n=1)

Generate multivariate random variable sample from a t-Student distribution.

Original code by Enzo Michelangeli. Modified by Luis C. Garcia-Peraza Herrera. This static method is exclusively used by ‘tests/smm_test.py’.

Parameters:

• m (array_like, shape (n_features,).) – Mean vector, its length determines the dimension of the random variable.
• S (array_like, shape (n_features, n_features).) – Covariance matrix.
• df (int or float.) – Degrees of freedom.
• n (int.) – Number of observations.

Returns:

rvs – Each row is an independent draw of a multivariate t distributed random variable.

Return type:

array_like, shape (n, len(m))

predict(X)

Predict label for data.

This function will tell you which component of the mixture most likely generated the sample.

Parameters:X (array-like, shape (n_samples, n_features).) Returns:r_argmax Return type:array_like, shape (n_samples,)

predict_proba(X)

Predict label for data.

This function will tell the probability of each component generating each sample.

Parameters:X (array-like, shape (n_samples, n_features).) Returns:responsibilities Return type:array_like, shape (n_samples, n_components)

score(X, y=None)

Compute the log probability under the model.

Parameters:X (array_like, shape (n_samples, n_features).) Returns:prob – Probabilities of each data point in X. Return type:array_like, shape (n_samples,)

score_samples(X)

Per-sample likelihood of the data under the model.

Compute the probability of X under the model and return the posterior distribution (responsibilities) of each mixture component for each element of X.

Parameters:X (array_like, shape (n_samples, n_features).) Returns:

• prob (array_like, shape (n_samples,).) – Unnormalised probability of each data point in X, i.e. likelihoods.
• responsibilities (array_like, shape (n_samples,) – n_components). Posterior probabilities of each mixture component for each observation.

weights

Returns the weights of each component in the mixture.

exception smm.dofMaximizationError(message)

Bases: exceptions.ValueError