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Algorithms and components for machine learning and statistics.
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/*
* File: MultinomialDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Dec 16, 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.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.MathUtil;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.math.matrix.VectorInputEvaluator;
import gov.sandia.cognition.statistics.AbstractDistribution;
import gov.sandia.cognition.statistics.ClosedFormComputableDiscreteDistribution;
import gov.sandia.cognition.statistics.ProbabilityMassFunction;
import gov.sandia.cognition.statistics.ProbabilityMassFunctionUtil;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.ObjectUtil;
import java.util.AbstractSet;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Iterator;
import java.util.Random;
/**
* A multinomial distribution is the multivariate/multiclass generalization
* of the Binomial distribution. That is, the PMF returns the probability of
* from "numTrials" trials of selecting from "numClasses" classes with
* the probabilities p1,p2,...p_numClasses. In our class, the probability
* parameters must be positive but do not have to sum to one because we
* normalize by the L1 norm.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Multinomial distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Multinomial_distribution"
)
public class MultinomialDistribution
extends AbstractDistribution
implements ClosedFormComputableDiscreteDistribution
{
/**
* Default number of classes (labels or parameters), {@value}.
*/
public static final int DEFAULT_NUM_CLASSES = 2;
/**
* Default number of trials, {@value}.
*/
public static final int DEFAULT_NUM_TRIALS = 1;
/**
* Number of trials in the distribution, must be greater than 0.
*/
private int numTrials;
/**
* Parameters of the multinomial distribution, must be at least
* 2-dimensional and each element must be nonnegative.
*/
private Vector parameters;
/**
* Creates a new instance of MultinomialDistribution
*/
public MultinomialDistribution()
{
this( DEFAULT_NUM_CLASSES, DEFAULT_NUM_TRIALS );
}
/**
* Creates a new instance of MultinomialDistribution
* @param numClasses
* Number of classes (labels or parameters) to use.
* @param numTrials
* Number of trials in the distribution, must be greater than 0.
*/
public MultinomialDistribution(
final int numClasses,
final int numTrials )
{
this( VectorFactory.getDefault().createVector(numClasses, 1.0),
numTrials );
}
/**
* Creates a new instance of MultinomialDistribution
* @param numTrials
* Number of trials in the distribution, must be greater than 0.
* @param parameters
* Parameters of the multinomial distribution, must be at least
* 2-dimensional and each element must be nonnegative.
*/
public MultinomialDistribution(
final Vector parameters,
final int numTrials )
{
this.setNumTrials(numTrials);
this.setParameters(parameters);
}
/**
* Copy constructor
* @param other
* MultinomialDistribution to copy
*/
public MultinomialDistribution(
final MultinomialDistribution other )
{
this( ObjectUtil.cloneSafe(other.getParameters()), other.getNumTrials() );
}
@Override
public MultinomialDistribution clone()
{
MultinomialDistribution clone = (MultinomialDistribution) super.clone();
clone.setParameters( ObjectUtil.cloneSafe(this.getParameters()) );
return clone;
}
/**
* Getter for parameters
* @return
* Parameters of the multinomial distribution, must be at least
* 2-dimensional and each element must be nonnegative.
*/
public Vector getParameters()
{
return this.parameters;
}
/**
* Setter for parameters
* @param parameters
* Parameters of the multinomial distribution, must be at least
* 2-dimensional and each element must be nonnegative.
*/
public void setParameters(
final Vector parameters)
{
final int N = parameters.getDimensionality();
if( N < 2 )
{
throw new IllegalArgumentException( "Dimensionality must be >= 2" );
}
for( int i = 0; i < N; i++ )
{
if( parameters.getElement(i) < 0.0 )
{
throw new IllegalArgumentException(
"All parameter elements must be >= 0.0" );
}
}
this.parameters = parameters;
}
@Override
public Vector convertToVector()
{
return ObjectUtil.cloneSafe(this.getParameters());
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertSameDimensionality( this.getParameters() );
this.setParameters( ObjectUtil.cloneSafe(parameters) );
}
/**
* Getter for numTrials
* @return
* Number of trials in the distribution, must be greater than 0.
*/
public int getNumTrials()
{
return this.numTrials;
}
/**
* Setter for numTrials
* @param numTrials
* Number of trials in the distribution, must be greater than 0.
*/
public void setNumTrials(
final int numTrials)
{
if( numTrials <= 0 )
{
throw new IllegalArgumentException( "numTrials must be > 0" );
}
this.numTrials = numTrials;
}
@Override
public Vector getMean()
{
return this.parameters.scale( this.numTrials/this.parameters.norm1() );
}
@Override
public void sampleInto(
final Random random,
final int sampleCount,
final Collection output)
{
final int numClasses = this.parameters.getDimensionality();
final double []probs = new double[ numClasses ];
final double probsum = this.parameters.norm1();
for( int j = 0; j < numClasses; j++ )
{
probs[j] = this.parameters.getElement(j) / probsum;
}
for( int n = 0; n < sampleCount; n++ )
{
double[] successes = new double[ numClasses ];
for( int i = 0; i < this.numTrials; i++ )
{
double p = random.nextDouble();
for( int k = 0; k < numClasses; k++ )
{
if( p <= probs[k] )
{
successes[k]++;
break;
}
p -= probs[k];
}
}
output.add( VectorFactory.getDefault().copyArray(successes) );
}
}
@Override
public MultinomialDistribution.Domain getDomain()
{
return new Domain(
this.getParameters().getDimensionality(), this.getNumTrials() );
}
@Override
public int getDomainSize()
{
return this.getDomain().size();
}
@Override
public MultinomialDistribution.PMF getProbabilityFunction()
{
return new MultinomialDistribution.PMF( this );
}
/**
* Probability Mass Function of the Multinomial Distribution.
*/
public static class PMF
extends MultinomialDistribution
implements ProbabilityMassFunction,
VectorInputEvaluator
{
/**
* Creates a new instance of MultinomialDistribution.PMF
*/
public PMF()
{
super();
}
/**
* Creates a new instance of MultinomialDistribution.PMF
* @param numClasses
* Number of classes (labels or parameters) to use.
* @param numTrials
* Number of trials in the distribution, must be greater than 0.
*/
public PMF(
final int numClasses,
final int numTrials )
{
super( numClasses, numTrials );
}
/**
* Creates a new instance of MultinomialDistribution.PMF
* @param numTrials
* Number of trials in the distribution, must be greater than 0.
* @param parameters
* Parameters of the multinomial distribution, must be at least
* 2-dimensional and each element must be nonnegative.
*/
public PMF(
final Vector parameters,
final int numTrials )
{
super( parameters, numTrials );
}
/**
* Copy constructor
* @param other
* MultinomialDistribution to copy
*/
public PMF(
MultinomialDistribution other )
{
super( other );
}
@Override
public int getInputDimensionality()
{
return this.getParameters().getDimensionality();
}
@Override
public Double evaluate(
final Vector input)
{
return Math.exp( this.logEvaluate(input) );
}
@Override
public double logEvaluate(
final Vector input)
{
final int N = this.getInputDimensionality();
input.assertDimensionalityEquals( N );
Vector p = this.getParameters();
double psum = p.norm1();
double logCoeff = MathUtil.logFactorial( this.getNumTrials() );
double logProb = 0.0;
int total = 0;
for( int i = 0; i < N; i++ )
{
int xi = (int) input.getElement(i);
total += xi;
double pi = p.getElement(i) / psum;
if( pi < 0.0 )
{
throw new IllegalArgumentException( "pi < 0.0" + p );
}
else if( pi == 0.0 )
{
// if we've got 0 probability and nonzero successes,
// then this is impossible: probability == 0.0
if( xi != 0 )
{
return Math.log(0.0);
}
}
else
{
if( xi != 0 )
{
logCoeff -= MathUtil.logFactorial(xi);
logProb += xi * Math.log(pi);
}
}
}
if( total != this.getNumTrials() )
{
throw new IllegalArgumentException(
"Integer input sum != num trials" );
}
return logCoeff + logProb;
}
@Override
public double getEntropy()
{
return ProbabilityMassFunctionUtil.getEntropy(this);
}
@Override
public MultinomialDistribution.PMF getProbabilityFunction()
{
return this;
}
}
/**
* Allows the iteration through the set of subsets. That is, how many ways
* can we label "numTrials" objects with "numClasses" labels. BE CAREFUL,
* before iterating through all members of a Domain, as this
* grows as a factorial!!! (See the size() method for the exact size.)
*/
public static class Domain
extends AbstractSet
{
/**
* Number of classes to sample from.
*/
private int numClasses;
/**
* Number of times to sample from the classes.
*/
private int numTrials;
/**
* Creates a new instance of Domain
* @param numClasses
* Number of classes to sample from.
* @param numTrials
* Number of times to sample from the classes.
*/
public Domain(
final int numClasses,
final int numTrials )
{
this.numClasses = numClasses;
this.numTrials = numTrials;
}
@Override
public Iterator iterator()
{
return new MultinomialIterator(this.numClasses,this.numTrials);
}
@Override
public int size()
{
return MathUtil.binomialCoefficient(
this.numClasses+this.numTrials-1,this.numClasses-1 );
}
/**
* The log of the size.
*
* @return
* The log of the size.
*/
public double logSize()
{
return MathUtil.logBinomialCoefficient(
this.numClasses+this.numTrials-1,this.numClasses-1 );
}
/**
* An Iterator over a Domain
*/
protected static class MultinomialIterator
extends AbstractCloneableSerializable
implements Iterator
{
/**
* Value at the head of the subset.
*/
private int value;
/**
* Number of classes to sample from.
*/
private int numClasses;
/**
* Number of times to sample from the classes.
*/
private int numTrials;
/**
* Child iterator for recursion.
*/
private MultinomialIterator child;
/**
* Creates a new instance of Domain
* @param numClasses
* Number of classes to sample from.
* @param numTrials
* Number of times to sample from the classes.
*/
public MultinomialIterator(
final int numClasses,
final int numTrials )
{
if( numClasses <= 0 )
{
throw new IllegalArgumentException( "NumClasses <= 0" );
}
this.numClasses = numClasses;
if( numTrials < 0 )
{
throw new IllegalArgumentException( "numTrials < 0" );
}
this.numTrials = numTrials;
if( this.numClasses <= 1 )
{
this.value = this.numTrials;
}
else
{
this.value = 0;
}
if( this.numClasses > 1 )
{
this.child = new MultinomialIterator(this.numClasses-1, this.numTrials-this.value );
}
}
@Override
public boolean hasNext()
{
if( this.value < this.numTrials )
{
return true;
}
else if( this.child == null )
{
return this.value <= this.numTrials;
}
else
{
return this.child.hasNext();
}
}
@Override
public Vector next()
{
if( this.child == null )
{
Vector subset = VectorFactory.getDefault().createVector(1,this.value);
this.value++;
return subset;
}
else
{
if( !this.child.hasNext() )
{
this.value++;
this.child = new MultinomialIterator(numClasses-1, this.numTrials-this.value);
}
return VectorFactory.getDefault().createVector(1,this.value).stack( this.child.next() );
}
}
@Override
public void remove()
{
throw new UnsupportedOperationException(
"Cannot remove from MultinomialDomain" );
}
}
}
}