smile.stat.distribution.ExponentialFamily Maven / Gradle / Ivy
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/*******************************************************************************
* Copyright (c) 2010 Haifeng Li
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/
package smile.stat.distribution;
/**
* The exponential family is a class of probability distributions sharing
* a certain form. The normal, exponential, gamma, chi-square, beta, Weibull
* (if the shape parameter is known), Dirichlet, Bernoulli, binomial,
* multinomial, Poisson, negative binomial, and geometric distributions
* are all exponential families. The family of Pareto distributions with
* a fixed minimum bound form an exponential family.
*
* The Cauchy, Laplace, and uniform families of distributions are not
* exponential families. The Weibull distribution is not an exponential
* family unless the shape parameter is known.
*
* The purpose of this interface is mainly to define the method M that is
* the Maximization step in the EM algorithm. Note that distributuions of exponential
* family has the close-form solutions in the EM algorithm. With this interface,
* we may allow the mixture contains distributions of different form as long as
* it is from exponential family.
*
* @see ExponentialFamilyMixture
* @see DiscreteExponentialFamily
* @see DiscreteExponentialFamilyMixture
*
* @author Haifeng Li
*/
public interface ExponentialFamily {
/**
* The M step in the EM algorithm, which depends the specific distribution.
*
* @param x the input data for estimation
* @param posteriori the posteriori probability.
* @return the (unnormalized) weight of this distribution in the mixture.
*/
Mixture.Component M(double[] x, double[] posteriori);
}