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/*
* File: NormalInverseWishartDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Mar 25, 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.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
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.AbstractDistribution;
import gov.sandia.cognition.statistics.ClosedFormComputableDistribution;
import gov.sandia.cognition.statistics.ProbabilityDensityFunction;
import gov.sandia.cognition.util.ObjectUtil;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* The normal inverse Wishart distribution
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Stanley Sawyer",
title="Wishart Distributions and Inverse-Wishart Sampling",
type=PublicationType.Misc,
year=2007,
url="http://www.math.wustl.edu/~sawyer/hmhandouts/Wishart.pdf"
)
public class NormalInverseWishartDistribution
extends AbstractDistribution
implements ClosedFormComputableDistribution
{
/**
* Default dimensionality of the precision matrix, {@value}.
*/
public static final int DEFAULT_DIMENSIONALITY = 2;
/**
* Default covariance divisor, {@value}.
*/
public static final double DEFAULT_COVARIANCE_DIVISOR = 1.0;
/**
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
protected double covarianceDivisor;
/**
* Generates the mean, given the covariance from the inverseWishart.
*/
protected MultivariateGaussian gaussian;
/**
* Generates the covariance for the Gaussian.
*/
protected InverseWishartDistribution inverseWishart;
/**
* Default constructor
*/
public NormalInverseWishartDistribution()
{
this( DEFAULT_DIMENSIONALITY );
}
/**
* Creates a new instance of NormalInverseWishartDistribution
* @param dimensionality
* Dimensionality of the distributions
*/
public NormalInverseWishartDistribution(
int dimensionality )
{
this( dimensionality, DEFAULT_COVARIANCE_DIVISOR );
}
/**
* Creates a new instance of NormalInverseWishartDistribution
* @param dimensionality
* Dimensionality of the distributions
* @param covarianceDivisor
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public NormalInverseWishartDistribution(
int dimensionality,
double covarianceDivisor )
{
this( new MultivariateGaussian( dimensionality ),
new InverseWishartDistribution( dimensionality ),
covarianceDivisor );
}
/**
* Creates a new instance of NormalInverseWishartDistribution
* @param gaussian
* Generates the mean, given the covariance from the inverseWishart.
* @param inverseWishart
* Generates the covariance for the Gaussian.
* @param covarianceDivisor
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public NormalInverseWishartDistribution(
MultivariateGaussian gaussian,
InverseWishartDistribution inverseWishart,
double covarianceDivisor )
{
this.setGaussian(gaussian);
this.setInverseWishart(inverseWishart);
this.setCovarianceDivisor(covarianceDivisor);
}
/**
* Copy constructor
* @param other
* NormalInverseWishartDistribution to copy
*/
public NormalInverseWishartDistribution(
NormalInverseWishartDistribution other )
{
this( ObjectUtil.cloneSafe( other.getGaussian() ),
ObjectUtil.cloneSafe( other.getInverseWishart() ),
other.getCovarianceDivisor() );
}
@Override
public NormalInverseWishartDistribution clone()
{
NormalInverseWishartDistribution clone =
(NormalInverseWishartDistribution) super.clone();
clone.setGaussian( ObjectUtil.cloneSafe( this.getGaussian() ) );
clone.setInverseWishart( ObjectUtil.cloneSafe( this.getInverseWishart() ) );
return clone;
}
/**
* Getter for gaussian.
* @return
* Generates the mean, given the covariance from the inverseWishart.
*/
public MultivariateGaussian getGaussian()
{
return this.gaussian;
}
/**
* Setter for gaussian
* @param gaussian
* Generates the mean, given the covariance from the inverseWishart.
*/
public void setGaussian(
MultivariateGaussian gaussian)
{
this.gaussian = gaussian;
}
/**
* Getter for inverseWishart
* @return
* Generates the covariance for the Gaussian.
*/
public InverseWishartDistribution getInverseWishart()
{
return this.inverseWishart;
}
/**
* Setter for inverseWishart
* @param inverseWishart
* Generates the covariance for the Gaussian.
*/
public void setInverseWishart(
InverseWishartDistribution inverseWishart)
{
this.inverseWishart = inverseWishart;
}
/**
* Getter for covarianceDivisor
* @return
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public double getCovarianceDivisor()
{
return this.covarianceDivisor;
}
/**
* Setter for covarianceDivisor
* @param covarianceDivisor
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public void setCovarianceDivisor(
double covarianceDivisor)
{
if( covarianceDivisor <= 0.0 )
{
throw new IllegalArgumentException(
"covarianceDivisor must be > 0.0" );
}
this.covarianceDivisor = covarianceDivisor;
}
public Matrix getMean()
{
Matrix C = this.inverseWishart.getMean();
Vector mean = this.gaussian.getMean();
final int d = this.getInputDimensionality();
Matrix R = MatrixFactory.getDefault().createMatrix(d, d+1);
R.setColumn(0, mean);
R.setSubMatrix(0, 1, C);
return R;
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
final int d = this.gaussian.getInputDimensionality();
ArrayList covariances =
this.inverseWishart.sample(random, sampleCount);
for( Matrix covariance : covariances )
{
Matrix meanAndCovariance =
MatrixFactory.getDefault().createMatrix(d,d+1);
meanAndCovariance.setSubMatrix(0, 1, covariance);
covariance.scaleEquals(1.0/this.covarianceDivisor);
this.gaussian.setCovariance(covariance);
Vector mean = this.gaussian.sample(random);
meanAndCovariance.setColumn(0, mean);
output.add( meanAndCovariance );
}
}
public Vector convertToVector()
{
Vector c = VectorFactory.getDefault().copyValues( this.covarianceDivisor );
c = c.stack( this.gaussian.getMean() );
return c.stack( this.inverseWishart.convertToVector() );
}
public void convertFromVector(
Vector parameters)
{
final int d = this.getInputDimensionality();
parameters.assertDimensionalityEquals( 1+d + 1+d*d );
this.setCovarianceDivisor( parameters.getElement(0) );
Vector mean = parameters.subVector(1, d);
this.gaussian.setMean(mean);
Vector iwp = parameters.subVector(d+1, parameters.getDimensionality()-1);
this.inverseWishart.convertFromVector(iwp);
}
/**
* Gets the input dimensionality of the Gaussian and the inverse-Wishart
* distributions
* @return
* Input dimensionality of the Gaussian and the inverse-Wishart
* distributions
*/
public int getInputDimensionality()
{
return (this.gaussian != null) ? this.gaussian.getInputDimensionality() : 0;
}
public NormalInverseWishartDistribution.PDF getProbabilityFunction()
{
return new NormalInverseWishartDistribution.PDF( this );
}
/**
* PDF of the normal inverse-Wishart distribution.
*/
public static class PDF
extends NormalInverseWishartDistribution
implements ProbabilityDensityFunction
{
/**
* Default constructor
*/
public PDF()
{
super();
}
/**
* Creates a new instance of NormalInverseWishartDistribution
* @param dimensionality
* Dimensionality of the distributions
* @param covarianceDivisor
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public PDF(
int dimensionality,
double covarianceDivisor )
{
super( dimensionality, covarianceDivisor );
}
/**
* Creates a new instance of NormalInverseWishartDistribution
* @param gaussian
* Generates the mean, given the covariance from the inverseWishart.
* @param inverseWishart
* Generates the covariance for the Gaussian.
* @param covarianceDivisor
* Term that divides the covariance sampled from the inverseWishart,
* must be greater than zero.
*/
public PDF(
MultivariateGaussian gaussian,
InverseWishartDistribution inverseWishart,
double covarianceDivisor )
{
super( gaussian, inverseWishart, covarianceDivisor );
}
/**
* Copy constructor
* @param other
* NormalInverseWishartDistribution to copy
*/
public PDF(
NormalInverseWishartDistribution other )
{
super( other );
}
@Override
public NormalInverseWishartDistribution.PDF getProbabilityFunction()
{
return this;
}
public double logEvaluate(
Matrix input)
{
final int d = input.getNumRows();
Vector mean = input.getColumn(0);
Matrix C = input.getSubMatrix(0,d-1,1,d);
C.scaleEquals(1.0/this.covarianceDivisor);
double lpg = this.gaussian.getProbabilityFunction().logEvaluate(mean);
double lpiw = this.inverseWishart.getProbabilityFunction().logEvaluate(C);
return lpg + lpiw;
}
public Double evaluate(
Matrix input)
{
return Math.exp( this.logEvaluate(input) );
}
}
}