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/*
* File: MultivariateGaussianMeanBayesianEstimator.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Nov 23, 2009, 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.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.math.ComplexNumber;
import gov.sandia.cognition.math.MultivariateStatisticsUtil;
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.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.bayesian.AbstractBayesianParameter;
import gov.sandia.cognition.statistics.bayesian.BayesianParameter;
import gov.sandia.cognition.statistics.distribution.MultivariateGaussian;
import java.util.Arrays;
/**
* Bayesian estimator for the mean of a MultivariateGaussian using its conjugate
* prior, which is also a MultivariateGaussian. This estimation method assumes
* that the covariance matrix of the estimated mean is known.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="William M. Bolstad",
title="Introduction to Bayesian Statistics: Second Edition",
type=PublicationType.Book,
year=2007,
pages={208}
)
public class MultivariateGaussianMeanBayesianEstimator
extends AbstractConjugatePriorBayesianEstimator
implements ConjugatePriorBayesianEstimatorPredictor
{
/**
* Default dimensionality, {@value}.
*/
public static final int DEFAULT_DIMENSIONALITY = 1;
/**
* Creates a new instance of MultivariateGaussianMeanBayesianEstimator
*/
public MultivariateGaussianMeanBayesianEstimator()
{
this( DEFAULT_DIMENSIONALITY );
}
/**
* Creates a new instance of MultivariateGaussianMeanBayesianEstimator
* @param dimensionality
* Dimensionality of the Vectors
*/
public MultivariateGaussianMeanBayesianEstimator(
int dimensionality )
{
this( MatrixFactory.getDefault().createIdentity(dimensionality,dimensionality) );
}
/**
* Creates a new instance of MultivariateGaussianMeanBayesianEstimator
* @param knownCovarianceInverse
* Known covariance matrix of the estimated mean.
*/
public MultivariateGaussianMeanBayesianEstimator(
Matrix knownCovarianceInverse )
{
this( knownCovarianceInverse, new MultivariateGaussian(
VectorFactory.getDefault().createVector(knownCovarianceInverse.getNumRows()),
MatrixFactory.getDefault().createIdentity(knownCovarianceInverse.getNumRows(), knownCovarianceInverse.getNumColumns()) ) );
}
/**
* Creates a new instance of MultivariateGaussianMeanBayesianEstimator
* @param knownCovarianceInverse
* Known covariance matrix inverse of the estimated mean. Sometimes
* called the "precision matrix".
* @param belief
* Belief distribution of the mean.
*/
public MultivariateGaussianMeanBayesianEstimator(
Matrix knownCovarianceInverse,
MultivariateGaussian belief )
{
this( new MultivariateGaussian(
VectorFactory.getDefault().createVector( knownCovarianceInverse.getNumRows() ),
knownCovarianceInverse.inverse() ),
belief );
}
/**
* Creates a new instance of PoissonBayesianEstimator
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public MultivariateGaussianMeanBayesianEstimator(
MultivariateGaussian conditional,
MultivariateGaussian prior )
{
this( new MultivariateGaussianMeanBayesianEstimator.Parameter(
conditional, prior) );
}
/**
* Creates a new instance
* @param parameter
* Bayesian hyperparameter relationship between the conditional
* distribution and the conjugate prior distribution.
*/
protected MultivariateGaussianMeanBayesianEstimator(
BayesianParameter parameter )
{
super( parameter );
}
public MultivariateGaussianMeanBayesianEstimator.Parameter createParameter(
MultivariateGaussian conditional,
MultivariateGaussian prior)
{
return new MultivariateGaussianMeanBayesianEstimator.Parameter( conditional, prior );
}
/**
* Getter for knownCovarianceInverse.
* @return
* Known covariance matrix inverse of the estimated mean. Sometimes
* called the "precision matrix".
*/
public Matrix getKnownCovarianceInverse()
{
return this.parameter.getConditionalDistribution().getCovarianceInverse();
}
/**
* Setter for knownCovarianceInverse.
* @param knownCovarianceInverse
* Known covariance matrix inverse of the estimated mean. Sometimes
* called the "precision matrix".
*/
public void setKnownCovarianceInverse(
Matrix knownCovarianceInverse)
{
if( !knownCovarianceInverse.isSymmetric() ||
(knownCovarianceInverse.rank() != knownCovarianceInverse.getNumRows()) )
{
throw new IllegalArgumentException(
"Covariance inverse must be symmetric and invertible!" );
}
this.parameter.getConditionalDistribution().setCovariance(
knownCovarianceInverse.inverse() );
}
@Override
public void update(
MultivariateGaussian target,
Iterable data)
{
int N = CollectionUtil.size(data);
Matrix Ci0 = target.getCovarianceInverse();
Matrix CiN = this.getKnownCovarianceInverse().clone();
if( N > 1 )
{
CiN.scaleEquals(N);
}
Vector sampleMean = MultivariateStatisticsUtil.computeMean(data);
Vector t0 = Ci0.times( target.getMean() );
t0.plusEquals( CiN.times( sampleMean ) );
// Saving another Matrix creation here... just make sure the
// "t0" stuff gets completed first
CiN.plusEquals(Ci0);
Matrix updatedCovariance = CiN.inverse();
Vector updatedMean = updatedCovariance.times( t0 );
target.setMean(updatedMean);
target.setCovariance(updatedCovariance);
}
public void update(
MultivariateGaussian updater,
Vector data)
{
this.update(updater, Arrays.asList(data) );
}
public double computeEquivalentSampleSize(
MultivariateGaussian belief)
{
// The ratio is R = det(KnownVariance) / det(beliefVariance)
// R = det(beliefVarianceInverse) / det(KnownVarianceInverse)
// log(R) = log(det(beliefVarianceInverse)) - log(det(KnownVarianceInverse))
// Effective sample size is then
// SS = exp(log(R)/N), where "N" is the dimensionality of the data.
ComplexNumber logR = belief.getCovarianceInverse().logDeterminant().minus(
this.getKnownCovarianceInverse().logDeterminant() );
return Math.exp(logR.getMagnitude()/belief.getMean().getDimensionality());
}
public MultivariateGaussian createPredictiveDistribution(
MultivariateGaussian posterior)
{
Vector mean = posterior.getMean().clone();
Matrix C = posterior.getCovariance().plus(
this.parameter.getConditionalDistribution().getCovariance() );
return new MultivariateGaussian( mean, C );
}
@Override
public MultivariateGaussian createConditionalDistribution(
Vector parameter)
{
parameter.assertDimensionalityEquals(
this.parameter.getConditionalDistribution().getInputDimensionality() );
return super.createConditionalDistribution(parameter);
}
/**
* Parameter of this conjugate prior relationship.
*/
public static class Parameter
extends AbstractBayesianParameter
{
/**
* Name of the parameter, {@value}.
*/
public static final String NAME = "mean";
/**
* Creates a new instance
* @param prior
* Default conjugate prior.
* @param conditional
* Conditional distribution of the conjugate prior.
*/
public Parameter(
MultivariateGaussian conditional,
MultivariateGaussian prior )
{
super( conditional, NAME, prior );
}
public void setValue(
Vector value)
{
value.assertDimensionalityEquals(
this.conditionalDistribution.getInputDimensionality() );
this.conditionalDistribution.setMean(value);
}
public Vector getValue()
{
return this.conditionalDistribution.getMean();
}
}
}