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/*
* File: MultivariateGaussianMeanCovarianceBayesianEstimator.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Mar 26, 2010, 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.bayesian.conjugate;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationReferences;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.math.MultivariateStatisticsUtil;
import gov.sandia.cognition.math.RingAccumulator;
import gov.sandia.cognition.math.matrix.Matrix;
import gov.sandia.cognition.math.matrix.MatrixFactory;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.statistics.bayesian.AbstractBayesianParameter;
import gov.sandia.cognition.statistics.bayesian.BayesianParameter;
import gov.sandia.cognition.statistics.distribution.MultivariateGaussian;
import gov.sandia.cognition.statistics.distribution.MultivariateStudentTDistribution;
import gov.sandia.cognition.statistics.distribution.NormalInverseWishartDistribution;
import gov.sandia.cognition.util.Pair;
import java.util.Arrays;
/**
* Performs robust estimation of both the mean and covariance of a
* MultivariateGaussian conditional distribution using the conjugate prior
* Normal-Inverse-Wishart distribution. The resulting predictive distribution
* for future data is a multivariate Student's t-distribution.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReferences(
references={
@PublicationReference(
author={
"Andrew Gelman",
"John B. Carlin",
"Hal S. Stern",
"Donald B. Rubin"
},
title="Bayesian Data Analysis, Second Edition",
type=PublicationType.Book,
year=2004,
pages={87,88}
)
,
@PublicationReference(
author="Wikipedia",
title="Conjugate Prior",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Conjugate_prior"
)
}
)
public class MultivariateGaussianMeanCovarianceBayesianEstimator
extends AbstractConjugatePriorBayesianEstimator
implements ConjugatePriorBayesianEstimatorPredictor
{
/**
* Creates a new instance of MultivariateGaussianMeanCovarianceBayesianEstimator
*/
public MultivariateGaussianMeanCovarianceBayesianEstimator()
{
this( new NormalInverseWishartDistribution() );
}
/**
* Creates a new instance of MultivariateGaussianMeanCovarianceBayesianEstimator
* @param dimensionality
* Dimensionality of the observations to consider.
*/
public MultivariateGaussianMeanCovarianceBayesianEstimator(
int dimensionality )
{
this( new NormalInverseWishartDistribution( dimensionality ) );
}
/**
* Creates a new instance of MultivariateGaussianMeanCovarianceBayesianEstimator
* @param belief
* Initial belief of the conditional parameters
*/
public MultivariateGaussianMeanCovarianceBayesianEstimator(
NormalInverseWishartDistribution belief )
{
this( new MultivariateGaussian( belief.getInputDimensionality() ), belief );
}
/**
* Creates a new instance
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public MultivariateGaussianMeanCovarianceBayesianEstimator(
MultivariateGaussian conditional,
NormalInverseWishartDistribution prior )
{
this( new MultivariateGaussianMeanCovarianceBayesianEstimator.Parameter(
conditional, prior) );
}
/**
* Creates a new instance
* @param parameter
* Bayesian hyperparameter relationship between the conditional
* distribution and the conjugate prior distribution.
*/
protected MultivariateGaussianMeanCovarianceBayesianEstimator(
BayesianParameter parameter )
{
super( parameter );
}
public MultivariateGaussianMeanCovarianceBayesianEstimator.Parameter createParameter(
MultivariateGaussian conditional,
NormalInverseWishartDistribution prior)
{
return new MultivariateGaussianMeanCovarianceBayesianEstimator.Parameter( conditional, prior );
}
public void update(
NormalInverseWishartDistribution target,
Vector data)
{
this.update(target, Arrays.asList(data) );
}
@Override
public void update(
NormalInverseWishartDistribution prior,
Iterable data)
{
final int n = CollectionUtil.size(data);
Pair pair =
MultivariateStatisticsUtil.computeMeanAndCovariance(data);
Vector sampleMean = pair.getFirst();
Matrix sampleCovariance = pair.getSecond();
Vector lambda = prior.getGaussian().getMean();
double nu = prior.getCovarianceDivisor();
int alpha = prior.getInverseWishart().getDegreesOfFreedom();
Matrix beta = prior.getInverseWishart().getInverseScale();
int alphahat = alpha + n;
double nuhat = nu+n;
Vector lambdahat = lambda.scale(nu/n);
lambdahat.plusEquals( sampleMean );
lambdahat.scaleEquals( n/nuhat );
Vector delta = sampleMean;
delta.minusEquals(lambda);
Matrix betahat = sampleCovariance;
if( n > 1 )
{
betahat.scaleEquals(n);
}
betahat.plusEquals(beta);
betahat.plusEquals( delta.outerProduct(delta.scale((n*nu)/nuhat)) );
prior.getGaussian().setMean(lambdahat);
prior.setCovarianceDivisor(nuhat);
prior.getInverseWishart().setDegreesOfFreedom(alphahat);
prior.getInverseWishart().setInverseScale(betahat);
}
public double computeEquivalentSampleSize(
NormalInverseWishartDistribution belief)
{
return belief.getCovarianceDivisor();
}
public MultivariateStudentTDistribution createPredictiveDistribution(
NormalInverseWishartDistribution posterior)
{
Vector mean = posterior.getGaussian().getMean();
double dofs = posterior.getInverseWishart().getDegreesOfFreedom()
- posterior.getInverseWishart().getInputDimensionality() + 1.0;
Matrix covariance = posterior.getInverseWishart().getInverseScale().scale(
(posterior.getCovarianceDivisor()+1.0) / (posterior.getCovarianceDivisor()*dofs) );
Matrix precision = covariance.inverse();
return new MultivariateStudentTDistribution( dofs, mean, precision );
}
/**
* Parameter for this conjugate prior estimator.
*/
public static class Parameter
extends AbstractBayesianParameter
{
/**
* Name of the parameter, {@value}.
*/
public static final String NAME = "meanAndCovariance";
/**
* Creates a new instance
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public Parameter(
MultivariateGaussian conditional,
NormalInverseWishartDistribution prior )
{
super( conditional, NAME, prior );
}
public void setValue(
Matrix value)
{
final int dim = this.conditionalDistribution.getInputDimensionality();
if( (value.getNumRows() != dim) ||
(value.getNumColumns() != (dim+1) ) )
{
throw new IllegalArgumentException( "Expected (dim x dim+1) Matrix" );
}
Vector mean = value.getColumn(0);
Matrix covariance = value.getSubMatrix(0, dim-1, 1,dim);
this.conditionalDistribution.setMean(mean);
this.conditionalDistribution.setCovariance(covariance);
}
public Matrix getValue()
{
final int dim = this.conditionalDistribution.getInputDimensionality();
Matrix parameter = MatrixFactory.getDefault().createMatrix(dim, dim+1);
parameter.setColumn(0, this.conditionalDistribution.getMean() );
parameter.setSubMatrix(0,1, this.conditionalDistribution.getCovariance() );
return parameter;
}
}
}