smile.stat.distribution

Class ExponentialFamilyMixture

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.Mixture

smile.stat.distribution.ExponentialFamilyMixture

All Implemented Interfaces:

java.io.Serializable, Distribution

Direct Known Subclasses:

GaussianMixture

public class ExponentialFamilyMixture
extends Mixture

The finite mixture of distributions from exponential family. The EM algorithm can be used to learn the mixture model from data. EM is particularly useful when the likelihood is an exponential family: the E-step becomes the sum of expectations of sufficient statistics, and the M-step involves maximizing a linear function. In such a case, it is usually possible to derive closed form updates for each step.

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class smile.stat.distribution.Mixture

Mixture.Component

Field Summary

Fields

Modifier and Type	Field and Description
double	bic The BIC score when the distribution is fit on a sample data.
double	L The log-likelihood when the distribution is fit on a sample data.

Fields inherited from class smile.stat.distribution.Mixture

components

Constructor Summary

Constructors

Constructor and Description
ExponentialFamilyMixture(Mixture.Component... components) Constructor.

Method Summary

Modifier and Type	Method and Description
static ExponentialFamilyMixture	fit(double[] x, Mixture.Component... components) Fits the mixture model with the EM algorithm.
static ExponentialFamilyMixture	fit(double[] x, Mixture.Component[] components, double gamma, int maxIter, double tol) Fits the mixture model with the EM algorithm.

Methods inherited from class smile.stat.distribution.Mixture

bic, cdf, entropy, length, logp, map, mean, p, posteriori, quantile, rand, size, toString, variance

Methods inherited from class smile.stat.distribution.AbstractDistribution

inverseTransformSampling, quantile, quantile, rejection

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface smile.stat.distribution.Distribution

likelihood, logLikelihood, rand, sd

Field Detail

L

public final double L

The log-likelihood when the distribution is fit on a sample data.

bic

public final double bic

The BIC score when the distribution is fit on a sample data.

Constructor Detail

ExponentialFamilyMixture

public ExponentialFamilyMixture(Mixture.Component... components)

Constructor.

Parameters:

components - a list of exponential family distributions.

Method Detail

fit

public static ExponentialFamilyMixture fit(double[] x,
                                           Mixture.Component... components)

Fits the mixture model with the EM algorithm.

Parameters:

components - the initial configuration of mixture. Components may have different distribution form.

x - the training data.

fit

public static ExponentialFamilyMixture fit(double[] x,
                                           Mixture.Component[] components,
                                           double gamma,
                                           int maxIter,
                                           double tol)

Fits the mixture model with the EM algorithm.

Parameters:

components - the initial configuration.

x - the training data.

gamma - the regularization parameter. Although regularization works well for high dimensional data, it often reduces the model to too few components. For one-dimensional data, gamma should be 0 in general.

maxIter - the maximum number of iterations.

tol - the tolerance of convergence test.