BayesianGaussianMixture #

classsklearn.mixture.BayesianGaussianMixture(*,n_components=1,covariance_type='full',tol=0.001,reg_covar=1e-06,max_iter=100,n_init=1,init_params='kmeans',weight_concentration_prior_type='dirichlet_process',weight_concentration_prior=None,mean_precision_prior=None,mean_prior=None,degrees_of_freedom_prior=None,covariance_prior=None,random_state=None,warm_start=False,verbose=0,verbose_interval=10)[source]#

Variational Bayesian estimation of a Gaussian mixture.

This class allows to infer an approximate posterior distribution over theparameters of a Gaussian mixture distribution. The effective number ofcomponents can be inferred from the data.

This class implements two types of prior for the weights distribution: afinite mixture model with Dirichlet distribution and an infinite mixturemodel with the Dirichlet Process. In practice Dirichlet Process inferencealgorithm is approximated and uses a truncated distribution with a fixedmaximum number of components (called the Stick-breaking representation).The number of components actually used almost always depends on the data.

Added in version 0.18.

Read more in theUser Guide.

Parameters:

n_componentsint, default=1

The number of mixture components. Depending on the data and the valueof theweight_concentration_prior the model can decide to not useall the components by setting some componentweights_ to values veryclose to zero. The number of effective components is therefore smallerthan n_components.

covariance_type{‘full’, ‘tied’, ‘diag’, ‘spherical’}, default=’full’

String describing the type of covariance parameters to use.Must be one of:

‘full’ (each component has its own general covariance matrix),
‘tied’ (all components share the same general covariance matrix),
‘diag’ (each component has its own diagonal covariance matrix),
‘spherical’ (each component has its own single variance).

tolfloat, default=1e-3

The convergence threshold. EM iterations will stop when thelower bound average gain on the likelihood (of the training data withrespect to the model) is below this threshold.

reg_covarfloat, default=1e-6

Non-negative regularization added to the diagonal of covariance.Allows to assure that the covariance matrices are all positive.

max_iterint, default=100

The number of EM iterations to perform.

n_initint, default=1

The number of initializations to perform. The result with the highestlower bound value on the likelihood is kept.

init_params{‘kmeans’, ‘k-means++’, ‘random’, ‘random_from_data’}, default=’kmeans’

The method used to initialize the weights, the means and thecovariances. String must be one of:

‘kmeans’: responsibilities are initialized using kmeans.
‘k-means++’: use the k-means++ method to initialize.
‘random’: responsibilities are initialized randomly.
‘random_from_data’: initial means are randomly selected data points.

Changed in version v1.1:init_params now accepts ‘random_from_data’ and ‘k-means++’ asinitialization methods.

weight_concentration_prior_type{‘dirichlet_process’, ‘dirichlet_distribution’}, default=’dirichlet_process’

String describing the type of the weight concentration prior.

weight_concentration_priorfloat or None, default=None

The dirichlet concentration of each component on the weightdistribution (Dirichlet). This is commonly called gamma in theliterature. The higher concentration puts more mass inthe center and will lead to more components being active, while a lowerconcentration parameter will lead to more mass at the edge of themixture weights simplex. The value of the parameter must be greaterthan 0. If it is None, it’s set to1./n_components.

mean_precision_priorfloat or None, default=None

The precision prior on the mean distribution (Gaussian).Controls the extent of where means can be placed. Largervalues concentrate the cluster means aroundmean_prior.The value of the parameter must be greater than 0.If it is None, it is set to 1.

mean_priorarray-like, shape (n_features,), default=None

The prior on the mean distribution (Gaussian).If it is None, it is set to the mean of X.

degrees_of_freedom_priorfloat or None, default=None

The prior of the number of degrees of freedom on the covariancedistributions (Wishart). If it is None, it’s set ton_features.

covariance_priorfloat or array-like, default=None

The prior on the covariance distribution (Wishart).If it is None, the emiprical covariance prior is initialized using thecovariance of X. The shape depends oncovariance_type:

(n_features,n_features)if'full',(n_features,n_features)if'tied',(n_features)if'diag',floatif'spherical'

random_stateint, RandomState instance or None, default=None

Controls the random seed given to the method chosen to initialize theparameters (seeinit_params).In addition, it controls the generation of random samples from thefitted distribution (see the methodsample).Pass an int for reproducible output across multiple function calls.SeeGlossary.

warm_startbool, default=False

If ‘warm_start’ is True, the solution of the last fitting is used asinitialization for the next call of fit(). This can speed upconvergence when fit is called several times on similar problems.Seethe Glossary.

verboseint, default=0

Enable verbose output. If 1 then it prints the currentinitialization and each iteration step. If greater than 1 thenit prints also the log probability and the time neededfor each step.

verbose_intervalint, default=10

Number of iteration done before the next print.

Attributes:

weights_array-like of shape (n_components,)

The weights of each mixture components.

means_array-like of shape (n_components, n_features)

The mean of each mixture component.

covariances_array-like

The covariance of each mixture component.The shape depends oncovariance_type:

(n_components,)if'spherical',(n_features,n_features)if'tied',(n_components,n_features)if'diag',(n_components,n_features,n_features)if'full'

precisions_array-like

The precision matrices for each component in the mixture. A precisionmatrix is the inverse of a covariance matrix. A covariance matrix issymmetric positive definite so the mixture of Gaussian can beequivalently parameterized by the precision matrices. Storing theprecision matrices instead of the covariance matrices makes it moreefficient to compute the log-likelihood of new samples at test time.The shape depends oncovariance_type:

(n_components,)if'spherical',(n_features,n_features)if'tied',(n_components,n_features)if'diag',(n_components,n_features,n_features)if'full'

precisions_cholesky_array-like

The cholesky decomposition of the precision matrices of each mixturecomponent. A precision matrix is the inverse of a covariance matrix.A covariance matrix is symmetric positive definite so the mixture ofGaussian can be equivalently parameterized by the precision matrices.Storing the precision matrices instead of the covariance matrices makesit more efficient to compute the log-likelihood of new samples at testtime. The shape depends oncovariance_type:

(n_components,)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 of the best fit of inference was reached, False otherwise.

n_iter_int

Number of step used by the best fit of inference to reach theconvergence.

lower_bound_float

Lower bound value on the model evidence (of the training data) of thebest fit of inference.

lower_bounds_array-like of shape (n_iter_,)

The list of lower bound values on the model evidence from each iterationof the best fit of inference.

weight_concentration_prior_tuple or float

The dirichlet concentration of each component on the weightdistribution (Dirichlet). The type depends onweight_concentration_prior_type:

(float,float)if'dirichlet_process'(Betaparameters),floatif'dirichlet_distribution'(Dirichletparameters).

The higher concentration puts more mass inthe center and will lead to more components being active, while a lowerconcentration parameter will lead to more mass at the edge of thesimplex.

weight_concentration_array-like of shape (n_components,)

The dirichlet concentration of each component on the weightdistribution (Dirichlet).

mean_precision_prior_float

The precision prior on the mean distribution (Gaussian).Controls the extent of where means can be placed.Larger values concentrate the cluster means aroundmean_prior.If mean_precision_prior is set to None,mean_precision_prior_ is setto 1.

mean_precision_array-like of shape (n_components,)

The precision of each components on the mean distribution (Gaussian).

mean_prior_array-like of shape (n_features,)

The prior on the mean distribution (Gaussian).

degrees_of_freedom_prior_float

The prior of the number of degrees of freedom on the covariancedistributions (Wishart).

degrees_of_freedom_array-like of shape (n_components,)

The number of degrees of freedom of each components in the model.

covariance_prior_float or array-like

The prior on the covariance distribution (Wishart).The shape depends oncovariance_type:

(n_features,n_features)if'full',(n_features,n_features)if'tied',(n_features)if'diag',floatif'spherical'

n_features_in_int

Number of features seen duringfit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen duringfit. Defined only whenXhas feature names that are all strings.

Added in version 1.0.

See also

GaussianMixture: Finite Gaussian mixture fit with EM.

References

[1]

Bishop, Christopher M. (2006). “Pattern recognition and machinelearning”. Vol. 4 No. 4. New York: Springer.

[2]

Hagai Attias. (2000). “A Variational Bayesian Framework forGraphical Models”. In Advances in Neural Information ProcessingSystems 12.

[3]

Blei, David M. and Michael I. Jordan. (2006). “Variationalinference for Dirichlet process mixtures”. Bayesian analysis 1.1

Examples

>>>importnumpyasnp>>>fromsklearn.mixtureimportBayesianGaussianMixture>>>X=np.array([[1,2],[1,4],[1,0],[4,2],[12,4],[10,7]])>>>bgm=BayesianGaussianMixture(n_components=2,random_state=42).fit(X)>>>bgm.means_array([[2.49 , 2.29],       [8.45, 4.52 ]])>>>bgm.predict([[0,0],[9,3]])array([0, 1])

fit(X,y=None)[source]#

Estimate model parameters with the EM algorithm.

The method fits the modeln_init times and sets the parameters withwhich the model has the largest likelihood or lower bound. Within eachtrial, the method iterates between E-step and M-step formax_itertimes until the change of likelihood or lower bound is less thantol, otherwise, aConvergenceWarning is raised.Ifwarm_start isTrue, thenn_init is ignored and a singleinitialization is performed upon the first call. Upon consecutivecalls, training starts where it left off.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: The fitted mixture.

fit_predict(X,y=None)[source]#

Estimate model parameters using X and predict the labels for X.

The method fits the model n_init times and sets the parameters withwhich the model has the largest likelihood or lower bound. Within eachtrial, the method iterates between E-step and M-step formax_itertimes until the change of likelihood or lower bound is less thantol, otherwise, aConvergenceWarning israised. After fitting, it predicts the most probable label for theinput data points.

Added in version 0.20.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

labelsarray, shape (n_samples,): Component labels.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please checkUser Guide on how the routingmechanism works.

Returns:

routingMetadataRequest: AMetadataRequest encapsulatingrouting information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator andcontained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

predict(X)[source]#

Predict the labels for the data samples in X using trained model.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

labelsarray, shape (n_samples,): Component labels.

predict_proba(X)[source]#

Evaluate the components’ density for each sample.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

resparray, shape (n_samples, n_components): Density of each Gaussian component for each sample in X.

sample(n_samples=1)[source]#

Generate random samples from the fitted Gaussian distribution.

Parameters:

n_samplesint, default=1: Number of samples to generate.

Returns:

Xarray, shape (n_samples, n_features): Randomly generated sample.
yarray, shape (nsamples,): Component labels.

score(X,y=None)[source]#

Compute the per-sample average log-likelihood of the given data X.

Parameters:

Xarray-like of shape (n_samples, n_dimensions): List of n_features-dimensional data points. Each rowcorresponds to a single data point.
yIgnored: Not used, present for API consistency by convention.

Returns:

log_likelihoodfloat: Log-likelihood ofX under the Gaussian mixture model.

score_samples(X)[source]#

Compute the log-likelihood of each sample.

Parameters:

Xarray-like of shape (n_samples, n_features): List of n_features-dimensional data points. Each rowcorresponds to a single data point.

Returns:

log_probarray, shape (n_samples,): Log-likelihood of each sample inX under the current model.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects(such asPipeline). The latter haveparameters of the form<component>__<parameter> so that it’spossible to update each component of a nested object.

Parameters: