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/*
* File: MultivariateGaussian.java
* Authors: Justin Basilico and Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright February 28, 2006, 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.CodeReview;
import gov.sandia.cognition.annotation.CodeReviewResponse;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.ComplexNumber;
import gov.sandia.cognition.math.MultivariateStatisticsUtil;
import gov.sandia.cognition.math.matrix.VectorFactory;
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.VectorInputEvaluator;
import gov.sandia.cognition.math.matrix.mtj.DenseMatrixFactoryMTJ;
import gov.sandia.cognition.math.matrix.mtj.decomposition.CholeskyDecompositionMTJ;
import gov.sandia.cognition.statistics.AbstractDistribution;
import gov.sandia.cognition.statistics.AbstractIncrementalEstimator;
import gov.sandia.cognition.statistics.AbstractSufficientStatistic;
import gov.sandia.cognition.statistics.ClosedFormComputableDistribution;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.DistributionWeightedEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.ProbabilityDensityFunction;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.ObjectUtil;
import gov.sandia.cognition.util.Pair;
import gov.sandia.cognition.util.WeightedValue;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* The MultivariateGaussian class implements a multidimensional Gaussian
* distribution that contains a mean vector and a covariance matrix. If your
* underlying distribution is univariate (scalar), then use the
* UnivariateGaussian class, as its operations are MUCH less computationally
* intensive.
*
* @author Justin Basilico
* @author Kevin R. Dixon
* @since 1.0
*/
@CodeReview(
reviewer = "Jonathan McClain",
date = "2006-05-15",
changesNeeded = true,
comments =
{
"A few minor changes needed.",
"Comments indicated with a / / / comment in the first column."
},
response = @CodeReviewResponse(
respondent = "Kevin R. Dixon",
date = "2006-05-15",
moreChangesNeeded = false,
comments = "Fixed."
)
)
@PublicationReference(
author = "Wikipedia",
title = "Multivariate normal distribution",
type = PublicationType.WebPage,
year = 2009,
url = "http://en.wikipedia.org/wiki/Multivariate_normal_distribution"
)
public class MultivariateGaussian
extends AbstractDistribution
implements ClosedFormComputableDistribution,
EstimableDistribution
{
/**
* Tolerance check for symmetry covariance tolerance, {@value}.
*/
public static final double DEFAULT_COVARIANCE_SYMMETRY_TOLERANCE = 1e-5;
/**
* Default dimensionality of the Gaussian, {@value}
*/
public static final int DEFAULT_DIMENSIONALITY = 2;
/**
* Natural logarithm of 2pi.
*/
public static final double LOG_TWO_PI = Math.log(2 * Math.PI);
/**
* Mean of the MultivariateGaussian.
*/
private Vector mean;
/**
* Covariance matrix of the MultivariateGaussian.
*/
private Matrix covariance;
/**
* Natural logarithm of the covariance matrix, automatically computed.
*/
private Double logCovarianceDeterminant;
/**
* Inverse of the covariance matrix, automatically computed.
*/
private Matrix covarianceInverse;
/**
* Natural logarithm of the leading likelihood coefficient, automatically
* computed.
*/
private Double logLeadingCoefficient;
/**
* Default constructor.
*/
public MultivariateGaussian()
{
this(DEFAULT_DIMENSIONALITY);
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param dimensionality Dimensionality of the Gaussian to create.
*/
public MultivariateGaussian(
int dimensionality)
{
this(VectorFactory.getDefault().createVector(dimensionality),
MatrixFactory.getDefault().createIdentity(dimensionality,
dimensionality));
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param mean The mean of the Gaussian distribution.
* @param covariance The covariance matrix, which should be a symmetric
* matrix.
*/
public MultivariateGaussian(
Vector mean,
Matrix covariance)
{
this.setMean(mean);
this.setCovariance(covariance);
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param other The other MultivariateGaussian to copy.
*/
public MultivariateGaussian(
MultivariateGaussian other)
{
this(ObjectUtil.cloneSafe(other.getMean()),
ObjectUtil.cloneSafe(other.getCovariance()));
}
@Override
public MultivariateGaussian clone()
{
MultivariateGaussian clone = (MultivariateGaussian) super.clone();
clone.setMean(ObjectUtil.cloneSafe(this.getMean()));
clone.setCovariance(ObjectUtil.cloneSafe(this.getCovariance()));
return clone;
}
@Override
public MultivariateGaussian.PDF getProbabilityFunction()
{
return new MultivariateGaussian.PDF(this);
}
/**
* Computes the z value squared, such that p(x) = coefficient *
* exp{-0.5*z^2}
*
* @param input input about which to compute the z-value squared
* @return z-value squared
*/
public double computeZSquared(
Vector input)
{
double zsquared;
// Subtract the mean
Vector delta = input.minus(this.mean);
// Compute the weighted inner product.
zsquared = delta.times(this.getCovarianceInverse()).dotProduct(
delta);
return zsquared;
}
/**
* Multiplies this Gaussian with the other Gaussian. This is also equivalent
* to computing the posterior belief using one of the Gaussians as the prior
* and one as the conditional likelihood.
*
* @param other Other Gaussian to multiply with this.
* @return Multiplied Gaussians.
*/
public MultivariateGaussian times(
MultivariateGaussian other)
{
Vector m1 = this.mean;
Matrix c1inv = this.getCovarianceInverse();
Vector m2 = other.getMean();
Matrix c2inv = other.getCovarianceInverse();
Matrix Cinv = c1inv.plus(c2inv);
Matrix C = Cinv.inverse();
Vector m = C.times(
c1inv.times(m1).plus(c2inv.times(m2)));
return new MultivariateGaussian(m, C);
}
/**
* Convolves this Gaussian with the other Gaussian.
*
* @param other Other Gaussian to convolve with this.
* @return Convolved Gaussians.
*/
public MultivariateGaussian convolve(
MultivariateGaussian other)
{
Vector meanHat = this.mean.plus(other.getMean());
Matrix covarianceHat = this.getCovariance().plus(other.getCovariance());
return new MultivariateGaussian(meanHat, covarianceHat);
}
/**
* Gets the dimensionality of the Gaussian. This is the expected
* dimensionality of the vectors that can be used with the Gaussian.
*
* @return The dimensionality of the multivariate Gaussian.
*/
public int getInputDimensionality()
{
return (this.mean != null) ? this.mean.getDimensionality() : 0;
}
@Override
public Vector getMean()
{
return this.mean;
}
/**
* Sets the mean vector.
*
* @param mean The new mean, throws NullPointerException if null
*/
public void setMean(
Vector mean)
{
if (mean == null)
{
throw new NullPointerException("Mean cannot be null.");
}
this.mean = mean;
}
/**
* Gets the covariance matrix of the Gaussian.
*
* @return The covariance matrix of the Gaussian.
*/
public Matrix getCovariance()
{
if (this.covariance == null)
{
this.covariance = this.covarianceInverse.inverse();
}
return this.covariance;
}
/**
* Sets the covariance matrix.
*
* @param covariance The new covariance matrix, the method forces the matrix
* to be symmetric by averaging the off-diagonal components into a clone of
* this parameter.
*/
public void setCovariance(
Matrix covariance)
{
this.setCovariance(covariance, DEFAULT_COVARIANCE_SYMMETRY_TOLERANCE);
}
/**
* Sets the covariance matrix.
*
* @param covariance The new covariance matrix, the method forces the matrix
* to be symmetric by averaging the off-diagonal components into a clone of
* this parameter.
* @param symmetryTolerance Tolerance for symmetry check
*/
public void setCovariance(
Matrix covariance,
double symmetryTolerance)
{
if (!covariance.isSymmetric(symmetryTolerance))
{
covariance = covariance.clone();
int N = covariance.getNumRows();
for (int i = 1; i < N; i++)
{
for (int j = 0; j < i; j++)
{
double vij = covariance.getElement(i, j);
double vji = covariance.getElement(j, i);
if (vij != vji)
{
double v = (vij + vji) / 2.0;
covariance.setElement(i, j, v);
covariance.setElement(j, i, v);
}
}
}
}
this.covariance = covariance;
// Flag the other values for recomputation...
this.covarianceInverse = null;
this.logCovarianceDeterminant = null;
this.logLeadingCoefficient = null;
}
/**
* Gets the inverse of the covariance matrix.
*
* @return The inverse of the covariance matrix.
*/
public Matrix getCovarianceInverse()
{
// Need to recompute the covariance inverse.
if (this.covarianceInverse == null)
{
this.covarianceInverse = this.covariance.inverse();
}
return this.covarianceInverse;
}
/**
* Sets the covariance inverse
*
* @param covarianceInverse Inverse of the covariance matrix
*/
public void setCovarianceInverse(
Matrix covarianceInverse)
{
this.setCovarianceInverse(covarianceInverse,
DEFAULT_COVARIANCE_SYMMETRY_TOLERANCE);
}
/**
* Sets the covariance inverse
*
* @param covarianceInverse Inverse of the covariance matrix
* @param symmetryTolerance Tolerance to enforce symmetry
*/
public void setCovarianceInverse(
Matrix covarianceInverse,
double symmetryTolerance)
{
if (!covarianceInverse.isSymmetric(symmetryTolerance))
{
covarianceInverse = covarianceInverse.clone();
int N = covarianceInverse.getNumRows();
for (int i = 1; i < N; i++)
{
for (int j = 0; j < i; j++)
{
final double vij = covarianceInverse.getElement(i, j);
final double vji = covarianceInverse.getElement(j, i);
if (vij != vji)
{
final double v = (vij + vji) / 2.0;
covarianceInverse.setElement(i, j, v);
covarianceInverse.setElement(j, i, v);
}
}
}
}
this.covarianceInverse = covarianceInverse;
// Flag the other values for recomputation...
this.covariance = null;
this.logCovarianceDeterminant = null;
this.logLeadingCoefficient = null;
}
/**
* Getter for logCovarianceDeterminant
*
* @return Natural logarithm of the covariance matrix, automatically
* computed.
*/
public double getLogCovarianceDeterminant()
{
if (this.logCovarianceDeterminant == null)
{
// Compute the determinant of the matrix.
ComplexNumber logDeterminant = this.covariance.logDeterminant();
// There should be no imaginary part, as the the determinant is
// a positive value
this.logCovarianceDeterminant = logDeterminant.getRealPart();
}
return this.logCovarianceDeterminant;
}
/**
* Getter for logLeadingCoefficient
*
* @return Natural logarithm of the leading likelihood coefficient,
* automatically computed.
*/
public double getLogLeadingCoefficient()
{
if (this.logLeadingCoefficient == null)
{
final int k = this.getInputDimensionality();
this.logLeadingCoefficient = (-0.5 * k * LOG_TWO_PI) + (-0.5
* this.getLogCovarianceDeterminant());
}
return this.logLeadingCoefficient;
}
@Override
public boolean equals(
Object randomVariable)
{
boolean retval = false;
if (randomVariable instanceof MultivariateGaussian)
{
MultivariateGaussian other = (MultivariateGaussian) randomVariable;
retval = (this.getMean().equals(other.getMean()))
&& (this.getCovariance().equals(other.getCovariance()));
}
return retval;
}
@Override
public int hashCode()
{
int hash = 7;
hash = 53 * hash + ObjectUtil.hashCodeSafe(this.mean);
hash = 53 * hash + ObjectUtil.hashCodeSafe(this.getCovariance());
return hash;
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
final Matrix covSqrt = CholeskyDecompositionMTJ.create(
DenseMatrixFactoryMTJ.INSTANCE.copyMatrix(this.getCovariance())).getR();
sampleInto(this.mean, covSqrt, random, sampleCount, output);
}
/**
* Returns a collection of draws this Gaussian with the given mean and
* covariance. If you need random draws from a Gaussian many times, I would
* recommend that you cache the square-root decomposition of the covariance
* and pass that to the method randomCovarianceSquareRoot().
*
* @param mean mean of the Gaussian
* @param covarianceSquareRoot square-root decomposition of the covariance
* of the Gaussian
* @param sampleCount number of times to draw from this random variable
* @param random Random-number generator
* @return ArrayList of Vectors drawn from this Gaussian distribution
*/
public static ArrayList sample(
Vector mean,
Matrix covarianceSquareRoot,
Random random,
int sampleCount)
{
final ArrayList result = new ArrayList(sampleCount);
sampleInto(mean, covarianceSquareRoot, random, sampleCount, result);
return result;
}
/**
* Performs a collection of draws this Gaussian with the given mean and
* covariance. If you need random draws from a Gaussian many times, I would
* recommend that you cache the square-root decomposition of the covariance
* and pass that to the method randomCovarianceSquareRoot().
*
* @param mean mean of the Gaussian
* @param covarianceSquareRoot square-root decomposition of the covariance
* of the Gaussian
* @param sampleCount number of times to draw from this random variable
* @param random Random-number generator
* @param output The collection to put the samples into.
*/
public static void sampleInto(
final Vector mean,
final Matrix covarianceSquareRoot,
final Random random,
final int sampleCount,
final Collection output)
{
for (int n = 0; n < sampleCount; n++)
{
output.add(sample(mean, covarianceSquareRoot, random));
}
}
/**
* Returns a single draw from the Gaussian with the given mean and
* covariance.
*
* @param mean mean of the Gaussian
* @param covarianceSquareRoot square-root decomposition of the covariance
* of the Gaussian
* @param random Random-number generator
* @return Vector drawn from this Gaussian distribution
*/
public static Vector sample(
Vector mean,
Matrix covarianceSquareRoot,
Random random)
{
int M = covarianceSquareRoot.getNumRows();
Vector x = VectorFactory.getDefault().createVector(M);
for (int i = 0; i < M; i++)
{
x.setElement(i, random.nextGaussian());
}
Vector sample = covarianceSquareRoot.times(x);
sample.plusEquals(mean);
return sample;
}
/**
* Scales the MultivariateGaussian by premultiplying by the given Matrix
*
* @param premultiplyMatrix Matrix against which to premultiply this
* @return Scaled MultivariateGaussian
*/
public MultivariateGaussian scale(
Matrix premultiplyMatrix)
{
Vector m = premultiplyMatrix.times(this.mean);
Matrix C = premultiplyMatrix.times(this.getCovariance()).times(
premultiplyMatrix.transpose());
return new MultivariateGaussian(m, C);
}
/**
* Adds two MultivariateGaussian random variables together and returns the
* resulting MultivariateGaussian
*
* @param other MultivariateGaussian to add to this MultivariateGaussian
* @return Effective addition of the two MultivariateGaussian random
* variables
*/
public MultivariateGaussian plus(
MultivariateGaussian other)
{
Vector m = this.mean.plus(other.getMean());
Matrix C = this.getCovariance().plus(other.getCovariance());
return new MultivariateGaussian(m, C);
}
@Override
public String toString()
{
String retval = "Mean: " + this.getMean() + "\n"
+ "Covariance:\n" + this.getCovariance();
return retval;
}
@Override
public Vector convertToVector()
{
return this.mean.stack(this.getCovariance().convertToVector());
}
@Override
public void convertFromVector(
Vector parameters)
{
int N = this.getInputDimensionality();
this.setMean(parameters.subVector(0, N - 1));
Matrix m = this.getCovariance();
m.convertFromVector(
parameters.subVector(N, parameters.getDimensionality() - 1));
this.setCovariance(m);
}
@Override
public MultivariateGaussian.MaximumLikelihoodEstimator getEstimator()
{
return new MultivariateGaussian.MaximumLikelihoodEstimator();
}
/**
* PDF of a multivariate Gaussian
*/
public static class PDF
extends MultivariateGaussian
implements ProbabilityDensityFunction,
VectorInputEvaluator
{
/**
* Default constructor.
*/
public PDF()
{
super();
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param dimensionality Dimensionality of the Gaussian to create.
*/
public PDF(
int dimensionality)
{
super(dimensionality);
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param mean The mean of the Gaussian distribution.
* @param covariance The covariance matrix, which should be a symmetric
* matrix.
*/
public PDF(
Vector mean,
Matrix covariance)
{
super(mean, covariance);
}
/**
* Creates a new instance of MultivariateGaussian.
*
* @param other The other MultivariateGaussian to copy.
*/
public PDF(
MultivariateGaussian other)
{
super(other);
}
@Override
public Double evaluate(
Vector input)
{
return Math.exp(this.logEvaluate(input));
}
@Override
public double logEvaluate(
Vector input)
{
double zsquared = this.computeZSquared(input);
return this.getLogLeadingCoefficient() - 0.5 * zsquared;
}
@Override
public MultivariateGaussian.PDF getProbabilityFunction()
{
return this;
}
}
/**
* Computes the Maximum Likelihood Estimate of the MultivariateGaussian
* given a set of Vectors
*/
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default covariance used in estimation, {@value}.
*/
public static final double DEFAULT_COVARIANCE
= UnivariateGaussian.MaximumLikelihoodEstimator.DEFAULT_VARIANCE;
/**
* Amount to add to the diagonal of the covariance matrix
*/
private double defaultCovariance;
/**
* Default constructor;
*/
public MaximumLikelihoodEstimator()
{
this(DEFAULT_COVARIANCE);
}
/**
* Creates a new instance of MaximumLikelihoodEstimator
*
* @param defaultCovariance Amount to add to the diagonal of the
* covariance matrix
*/
public MaximumLikelihoodEstimator(
double defaultCovariance)
{
this.defaultCovariance = defaultCovariance;
}
/**
* Computes the Gaussian that estimates the maximum likelihood of
* generating the given set of samples.
*
* @return The Gaussian that estimates the maximum likelihood of
* generating the given data.
* @param defaultCovariance amount to add to the diagonals of the
* covariance matrix, typically on the order of 1e-4, can be 0.0.
* @param data The samples to calculate the Gaussian from throws
* IllegalArgumentException if samples has 1 or fewer samples.
*/
public static MultivariateGaussian.PDF learn(
Collection data,
final double defaultCovariance)
{
final int N = data.size();
if (N <= 1)
{
throw new IllegalArgumentException(
"Need at least 2 data points to compute covariance");
}
Pair mle
= MultivariateStatisticsUtil.computeMeanAndCovariance(data);
Vector mean = mle.getFirst();
Matrix covariance = mle.getSecond();
// Add "defaultCovariance" to the diagonal entries
if (defaultCovariance != 0.0)
{
final int M = mean.getDimensionality();
for (int i = 0; i < M; i++)
{
double v = covariance.getElement(i, i);
covariance.setElement(i, i, v + defaultCovariance);
}
}
return new MultivariateGaussian.PDF(mean, covariance);
}
/**
* Computes the Gaussian that estimates the maximum likelihood of
* generating the given set of samples.
*
* @return The Gaussian that estimates the maximum likelihood of
* generating the given data.
* @param data The samples to calculate the Gaussian from throws
* IllegalArgumentException if samples has 1 or fewer samples.
*/
@Override
public MultivariateGaussian.PDF learn(
Collection data)
{
return MaximumLikelihoodEstimator.learn(
data, this.defaultCovariance);
}
}
/**
* Computes the Weighted Maximum Likelihood Estimate of the
* MultivariateGaussian given a weighted set of Vectors
*/
public static class WeightedMaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements
DistributionWeightedEstimator
{
/**
* Default covariance used in estimation, {@value}.
*/
public static final double DEFAULT_COVARIANCE
= MaximumLikelihoodEstimator.DEFAULT_COVARIANCE;
/**
* Amount to add to the diagonal of the covariance matrix
*/
private double defaultCovariance;
/**
* Default constructor.
*/
public WeightedMaximumLikelihoodEstimator()
{
this(DEFAULT_COVARIANCE);
}
/**
* Creates a new instance of WeightedMaximumLikelihoodEstimator
*
* @param defaultCovariance Amount to add to the diagonal of the
* covariance matrix
*/
public WeightedMaximumLikelihoodEstimator(
double defaultCovariance)
{
this.defaultCovariance = defaultCovariance;
}
/**
* Computes the Gaussian that estimates the maximum likelihood of
* generating the given set of weighted samples.
*
* @return The Gaussian that estimates the maximum likelihood of
* generating the given weighted data.
* @param data The weighted samples to calculate the Gaussian from
* throws IllegalArgumentException if samples has 1 or fewer samples.
*/
@Override
public MultivariateGaussian.PDF learn(
Collection> data)
{
return WeightedMaximumLikelihoodEstimator.learn(
data, this.defaultCovariance);
}
/**
* Computes the Gaussian that estimates the maximum likelihood of
* generating the given set of weighted samples.
*
*
* @return The Gaussian that estimates the maximum likelihood of
* generating the given weighted data.
* @param defaultCovariance Amount to add to the diagonal of the
* covariance matrix
* @param data The weighted samples to calculate the Gaussian from
* throws IllegalArgumentException if samples has 1 or fewer samples.
*/
public static MultivariateGaussian.PDF learn(
Collection> data,
final double defaultCovariance)
{
// Make sure there are enough samples.
final int N = data.size();
if (N <= 1)
{
// Error: Not enough samples.
throw new IllegalArgumentException(
"The number of samples must be greater than 1.");
}
Pair mle
= MultivariateStatisticsUtil.computeWeightedMeanAndCovariance(
data);
Vector mean = mle.getFirst();
Matrix covariance = mle.getSecond();
if (defaultCovariance != 0.0)
{
final int M = covariance.getNumRows();
for (int i = 0; i < M; i++)
{
final double v = covariance.getElement(i, i);
covariance.setElement(i, i, v + defaultCovariance);
}
}
return new MultivariateGaussian.PDF(mean, covariance);
}
}
/**
* Implements the sufficient statistics of the MultivariateGaussian.
*/
public static class SufficientStatistic
extends AbstractSufficientStatistic
{
/**
* Default covariance of the statistics, {@value}.
*/
public static final double DEFAULT_COVARIANCE
= MaximumLikelihoodEstimator.DEFAULT_COVARIANCE;
/**
* The mean of the Gaussian
*/
private Vector mean;
/**
* This is the sum-squared differences
*/
private Matrix sumSquaredDifferences;
/**
* Default covariance of the distribution
*/
protected double defaultCovariance;
/**
* Default constructor
*/
public SufficientStatistic()
{
this(DEFAULT_COVARIANCE);
}
/**
* Creates a new instance of SufficientStatistic
*
* @param defaultCovariance Default covariance of the distribution
*/
public SufficientStatistic(
double defaultCovariance)
{
super();
this.clear();
this.defaultCovariance = defaultCovariance;
}
@Override
public MultivariateGaussian.SufficientStatistic clone()
{
return (MultivariateGaussian.SufficientStatistic) super.clone();
}
/**
* Resets this set of sufficient statistics to its empty state.
*/
public void clear()
{
this.count = 0;
this.mean = null;
this.sumSquaredDifferences = null;
}
@Override
public void update(
Vector value)
{
// We've added another value.
this.count++;
// Compute the difference between the value and the current mean.
final int dim = value.getDimensionality();
if (this.mean == null)
{
this.mean = VectorFactory.getDefault().createVector(dim);
}
Vector delta = value.minus(this.mean);
// Update the mean based on the difference between the value
// and the mean along with the new count.
this.mean.plusEquals(delta.scale(1.0 / this.count));
// Update the squared differences from the mean, using the new
// mean in the process.
if (this.sumSquaredDifferences == null)
{
this.sumSquaredDifferences
= MatrixFactory.getDefault().createIdentity(dim, dim);
this.sumSquaredDifferences.scaleEquals(
this.getDefaultCovariance());
}
Vector delta2 = value.minus(this.mean);
this.sumSquaredDifferences.plusEquals(delta.outerProduct(delta2));
}
@Override
public MultivariateGaussian.PDF create()
{
return new MultivariateGaussian.PDF(
this.getMean(), this.getCovariance());
}
@Override
public void create(
MultivariateGaussian distribution)
{
distribution.setMean(this.getMean());
distribution.setCovariance(this.getCovariance());
}
/**
* Getter for defaultCovariance
*
* @return Default covariance of the distribution
*/
public double getDefaultCovariance()
{
return this.defaultCovariance;
}
/**
* Setter for defaultCovariance
*
* @param defaultCovariance Default covariance of the distribution
*/
public void setDefaultCovariance(
double defaultCovariance)
{
this.defaultCovariance = defaultCovariance;
}
/**
* Getter for mean
*
* @return The mean of the Gaussian
*/
public Vector getMean()
{
return this.mean;
}
/**
* Getter for sumSquaredDifferences
*
* @return This is the sum-squared differences
*/
public Matrix getSumSquaredDifferences()
{
return this.sumSquaredDifferences;
}
/**
* Gets the covariance of the Gaussian.
*
* @return The covariance.
*/
public Matrix getCovariance()
{
if (this.count <= 0)
{
return null;
}
else if (this.count == 1)
{
// This allows the default variance to be used.
return this.sumSquaredDifferences.clone();
}
else
{
return this.sumSquaredDifferences.scale(1.0 / (this.count - 1.0));
}
}
}
/**
* The estimator that creates a MultivariateGaussian from a stream of
* values.
*/
public static class IncrementalEstimator
extends AbstractIncrementalEstimator
{
/**
* Default covariance, {@value}.
*/
public static final double DEFAULT_COVARIANCE
= MaximumLikelihoodEstimator.DEFAULT_COVARIANCE;
/**
* Default covariance of the distribution
*/
private double defaultCovariance;
/**
* Default constructor
*/
public IncrementalEstimator()
{
this(DEFAULT_COVARIANCE);
}
/**
* Creates a new instance of IncrementalEstimator
*
* @param defaultCovariance Default covariance of the distribution
*/
public IncrementalEstimator(
double defaultCovariance)
{
super();
this.setDefaultCovariance(defaultCovariance);
}
/**
* Getter for defaultCovariance
*
* @return Default covariance of the distribution
*/
public double getDefaultCovariance()
{
return this.defaultCovariance;
}
/**
* Setter for defaultCovariance
*
* @param defaultCovariance Default covariance of the distribution
*/
public void setDefaultCovariance(
double defaultCovariance)
{
this.defaultCovariance = defaultCovariance;
}
@Override
public MultivariateGaussian.SufficientStatistic createInitialLearnedObject()
{
return new MultivariateGaussian.SufficientStatistic(
this.getDefaultCovariance());
}
}
/**
* Implements the sufficient statistics of the MultivariateGaussian while
* estimating the inverse of the covariance matrix. This is only slightly
* more computationally intensive than estimating the covariance directly,
* but does not require a single matrix inversion. This is useful when it's
* the covariance inverse ("precision") that you're interested in.
*/
@PublicationReference(
author = "Wikipedia",
title = "Sherman–Morrison formula",
type = PublicationType.WebPage,
year = 2011,
url = "http://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula"
)
public static class SufficientStatisticCovarianceInverse
extends AbstractSufficientStatistic
{
/**
* Default covariance of the statistics, {@value}.
*/
public static final double DEFAULT_COVARIANCE_INVERSE = 1.0
/ MultivariateGaussian.MaximumLikelihoodEstimator.DEFAULT_COVARIANCE;
/**
* The mean of the Gaussian
*/
private Vector mean;
/**
* This is the sum-squared differences
*/
private Matrix sumSquaredDifferencesInverse;
/**
* Default covariance inverse of the distribution
*/
protected double defaultCovarianceInverse;
/**
* Default constructor
*/
public SufficientStatisticCovarianceInverse()
{
this(DEFAULT_COVARIANCE_INVERSE);
}
/**
* Creates a new instance of SufficientStatisticCovarianceInverse
*
* @param defaultCovarianceInverse Default covariance inverse of the
* distribution
*/
public SufficientStatisticCovarianceInverse(
double defaultCovarianceInverse)
{
super();
this.clear();
this.defaultCovarianceInverse = defaultCovarianceInverse;
}
@Override
public SufficientStatisticCovarianceInverse clone()
{
return (SufficientStatisticCovarianceInverse) super.clone();
}
/**
* Resets this set of sufficient statistics to its empty state.
*/
public void clear()
{
this.count = 0;
this.mean = null;
this.sumSquaredDifferencesInverse = null;
}
@Override
public void update(
Vector value)
{
// We've added another value.
this.count++;
// Compute the difference between the value and the current mean.
final int dim = value.getDimensionality();
if (this.mean == null)
{
this.mean = VectorFactory.getDefault().createVector(dim);
}
Vector delta = value.minus(this.mean);
// Update the mean based on the difference between the value
// and the mean along with the new count.
this.mean.plusEquals(delta.scale(1.0 / this.count));
// Update the squared differences from the mean, using the new
// mean in the process.
if (this.sumSquaredDifferencesInverse == null)
{
this.sumSquaredDifferencesInverse
= MatrixFactory.getDefault().createIdentity(dim, dim);
this.sumSquaredDifferencesInverse.scaleEquals(
this.getDefaultCovarianceInverse());
}
Vector delta2 = value.minus(this.mean);
// This is the Sherman–Morrison formula:
// inv(A+uv') = inv(A)-(inv(A)uv'inv(A))/(1+v'inv(A)*u)
Vector Aiu = this.sumSquaredDifferencesInverse.times(delta);
Vector vtAi = delta2.times(this.sumSquaredDifferencesInverse);
double denom = 1.0 + delta2.dotProduct(Aiu);
vtAi.scaleEquals(1.0 / denom);
Matrix update = Aiu.outerProduct(vtAi);
this.sumSquaredDifferencesInverse.minusEquals(update);
}
@Override
public MultivariateGaussian.PDF create()
{
final Vector m = this.getMean();
MultivariateGaussian.PDF retval = new MultivariateGaussian.PDF(
m.getDimensionality());
retval.setMean(m);
retval.setCovarianceInverse(this.getCovarianceInverse());
return retval;
}
@Override
public void create(
MultivariateGaussian distribution)
{
distribution.setMean(this.getMean());
distribution.setCovarianceInverse(this.getCovarianceInverse());
}
/**
* Getter for defaultCovarianceInverse
*
* @return Default covariance Inverse of the distribution
*/
public double getDefaultCovarianceInverse()
{
return this.defaultCovarianceInverse;
}
/**
* Setter for defaultCovarianceInverse
*
* @param defaultCovarianceInverse Default covariance Inverse of the
* distribution
*/
public void setDefaultCovariance(
double defaultCovarianceInverse)
{
this.defaultCovarianceInverse = defaultCovarianceInverse;
}
/**
* Getter for mean
*
* @return The mean of the Gaussian
*/
public Vector getMean()
{
return this.mean;
}
/**
* Getter for sumSquaredDifferences
*
* @return This is the sum-squared differences
*/
public Matrix getSumSquaredDifferencesInverse()
{
return this.sumSquaredDifferencesInverse;
}
/**
* Gets the covariance Inverse of the Gaussian.
*
* @return The covariance.
*/
public Matrix getCovarianceInverse()
{
if (this.count <= 0)
{
return null;
}
else if (this.count == 1)
{
// This allows the default variance to be used.
return this.sumSquaredDifferencesInverse.clone();
}
else
{
return this.sumSquaredDifferencesInverse.scale(this.count - 1.0);
}
}
}
/**
* The estimator that creates a MultivariateGaussian from a stream of values
* by estimating the mean and covariance inverse (as opposed to the
* covariance directly), without ever performing a matrix inversion. This is
* useful when you're interested in the covariance inverse (precision)
* instead of the covariance itself.
*/
public static class IncrementalEstimatorCovarianceInverse
extends AbstractIncrementalEstimator
{
/**
* Default covariance Inverse, {@value}.
*/
public static final double DEFAULT_COVARIANCE_INVERSE = 1.0
/ MaximumLikelihoodEstimator.DEFAULT_COVARIANCE;
/**
* Default covariance Inverse of the distribution
*/
private double defaultCovarianceInverse;
/**
* Default constructor
*/
public IncrementalEstimatorCovarianceInverse()
{
this(DEFAULT_COVARIANCE_INVERSE);
}
/**
* Creates a new instance of IncrementalEstimatorCovarianceInverse
*
* @param defaultCovarianceInverse Default covariance Inverse of the
* distribution
*/
public IncrementalEstimatorCovarianceInverse(
double defaultCovarianceInverse)
{
super();
this.setDefaultCovarianceInverse(defaultCovarianceInverse);
}
/**
* Getter for defaultCovarianceInverse
*
* @return Default covariance Inverse of the distribution
*/
public double getDefaultCovarianceInverse()
{
return this.defaultCovarianceInverse;
}
/**
* Setter for defaultCovarianceInverse
*
* @param defaultCovarianceInverse Default covariance Inverse of the
* distribution
*/
public void setDefaultCovarianceInverse(
double defaultCovarianceInverse)
{
this.defaultCovarianceInverse = defaultCovarianceInverse;
}
@Override
public MultivariateGaussian.SufficientStatisticCovarianceInverse createInitialLearnedObject()
{
return new MultivariateGaussian.SufficientStatisticCovarianceInverse(
this.getDefaultCovarianceInverse());
}
}
}