/*
* File: MultivariateMixtureDensityModel.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Apr 12, 2011, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government.
* Export of this program may require a license from the United States
* Government. See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.statistics.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.RingAccumulator;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.ClosedFormComputableDistribution;
import gov.sandia.cognition.statistics.ProbabilityDensityFunction;
import gov.sandia.cognition.statistics.ProbabilityFunction;
import gov.sandia.cognition.util.ObjectUtil;
import java.util.Arrays;
import java.util.Collection;
/**
* A LinearMixtureModel of multivariate distributions with associated PDFs.
* @param <DistributionType>
* Type of Distribution in the mixture
* @author Kevin R. Dixon
* @since 3.1
*/
@PublicationReference(
author="Wikipedia",
title="Mixture Model",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Mixture_model"
)
public class MultivariateMixtureDensityModel<DistributionType extends ClosedFormComputableDistribution<Vector>>
extends LinearMixtureModel<Vector, DistributionType>
implements ClosedFormComputableDistribution<Vector>
{
/**
* Creates a new instance of MultivariateMixtureDensityModel
* @param distributions
* Underlying distributions from which we sample
*/
public MultivariateMixtureDensityModel(
Collection<? extends DistributionType> distributions )
{
this( distributions, null );
}
/**
* Creates a new instance of MultivariateMixtureDensityModel
* @param distributions
* Underlying distributions from which we sample
* @param priorWeights
* Weights proportionate by which the distributions are sampled
*/
public MultivariateMixtureDensityModel(
Collection<? extends DistributionType> distributions,
double[] priorWeights )
{
super( distributions, priorWeights );
}
/**
* Copy Constructor
* @param other
* MultivariateMixtureDensityModel to copy
*/
public MultivariateMixtureDensityModel(
MultivariateMixtureDensityModel<? extends DistributionType> other )
{
this( ObjectUtil.cloneSmartElementsAsArrayList(other.getDistributions()),
ObjectUtil.deepCopy(other.getPriorWeights()) );
}
@Override
public MultivariateMixtureDensityModel<DistributionType> clone()
{
return (MultivariateMixtureDensityModel<DistributionType>) super.clone();
}
@Override
public Vector getMean()
{
RingAccumulator<Vector> mean =
new RingAccumulator<Vector>();
final int K = this.getDistributionCount();
for( int k = 0; k < K; k++ )
{
mean.accumulate( this.getDistributions().get(k).getMean().scale(
this.getPriorWeights()[k] ) );
}
return mean.getSum().scale( 1.0 / this.getPriorWeightSum() );
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyArray(this.getPriorWeights());
}
@Override
public void convertFromVector(
Vector parameters)
{
parameters.assertDimensionalityEquals( this.getDistributionCount() );
for( int k = 0; k < parameters.getDimensionality(); k++ )
{
this.priorWeights[k] = parameters.getElement(k);
}
}
@Override
public MultivariateMixtureDensityModel.PDF<DistributionType> getProbabilityFunction()
{
return new MultivariateMixtureDensityModel.PDF<DistributionType>( this );
}
/**
* PDF of the MultivariateMixtureDensityModel
* @param <DistributionType>
* Type of Distribution in the mixture
*/
public static class PDF<DistributionType extends ClosedFormComputableDistribution<Vector>>
extends MultivariateMixtureDensityModel<DistributionType>
implements ProbabilityDensityFunction<Vector>
{
/**
* Creates a new instance of MultivariateMixtureDensityModel
* @param distributions
* Underlying distributions from which we sample
*/
public PDF(
Collection<? extends DistributionType> distributions )
{
super( distributions );
}
/**
* Creates a new instance of MultivariateMixtureDensityModel
* @param distributions
* Underlying distributions from which we sample
* @param priorWeights
* Weights proportionate by which the distributions are sampled
*/
public PDF(
Collection<? extends DistributionType> distributions,
double[] priorWeights )
{
super( distributions, priorWeights );
}
/**
* Copy Constructor
* @param other
* MultivariateMixtureDensityModel to copy
*/
public PDF(
MultivariateMixtureDensityModel<? extends DistributionType> other )
{
super( other );
}
@Override
public MultivariateMixtureDensityModel.PDF<DistributionType> getProbabilityFunction()
{
return this;
}
@Override
public double logEvaluate(
Vector input)
{
return Math.log( this.evaluate(input) );
}
@Override
public Double evaluate(
Vector input)
{
double sum = 0.0;
final int K = this.getDistributionCount();
for( int k = 0; k < K; k++ )
{
ProbabilityFunction<Vector> pdf =
this.getDistributions().get(k).getProbabilityFunction();
sum += pdf.evaluate(input) * this.priorWeights[k];
}
return sum/this.getPriorWeightSum();
}
/**
* Computes the probability distribution that the input was generated by
* the underlying distributions
* @param input Input to consider
* @return probability distribution that the input was generated by
* the underlying distributions
*/
public double[] computeRandomVariableProbabilities(
Vector input )
{
int K = this.getDistributionCount();
double[] likelihoods = this.computeRandomVariableLikelihoods( input );
double sum = 0.0;
for( int k = 0; k < K; k++ )
{
sum += likelihoods[k];
}
if( sum <= 0.0 )
{
Arrays.fill( likelihoods, 1.0/K );
}
sum = 0.0;
for( int k = 0; k < K; k++ )
{
likelihoods[k] *= this.priorWeights[k];
sum += likelihoods[k];
}
if( sum <= 0.0 )
{
Arrays.fill( likelihoods, 1.0/K );
sum = 1.0;
}
for( int k = 0; k < K; k++ )
{
likelihoods[k] /= sum;
}
return likelihoods;
}
/**
* Computes the likelihoods of the underlying distributions
* @param input Input to consider
* @return Vector of likelihoods for the underlying distributions
*/
public double[] computeRandomVariableLikelihoods(
Vector input )
{
int K = this.getDistributionCount();
double[] likelihoods = new double[ K ];
for( int k = 0; k < K; k++ )
{
ProbabilityFunction<Vector> pdf =
this.getDistributions().get(k).getProbabilityFunction();
likelihoods[k] = pdf.evaluate(input);
}
return likelihoods;
}
/**
* Gets the index of the most-likely distribution, given the input.
* That is, find the distribution that most likely generated the input
* @param input input to consider
* @return zero-based index of the most-likely distribution
*/
public int getMostLikelyRandomVariable(
Vector input )
{
double[] probabilities = this.computeRandomVariableProbabilities( input );
int bestIndex = 0;
double bestProbability = probabilities[0];
for( int i = 1; i < probabilities.length; i++ )
{
double prob = probabilities[i];
if( bestProbability < prob )
{
bestProbability = prob;
bestIndex = i;
}
}
return bestIndex;
}
}
}