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Algorithms and components for machine learning and statistics.
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/*
* File: ProbabilityMassFunctionUtil.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Feb 3, 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;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.learning.data.DefaultInputOutputPair;
import gov.sandia.cognition.learning.data.InputOutputPair;
import gov.sandia.cognition.math.ProbabilityUtil;
import gov.sandia.cognition.math.UnivariateStatisticsUtil;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.List;
import java.util.Random;
/**
* Utility methods for helping computations in PMFs.
* @author Kevin R. Dixon
* @since 3.0
*/
public class ProbabilityMassFunctionUtil
{
/**
* Computes the information-theoretic entropy of the PMF in bits.
* @param
* Type of data on the domain of the PMF.
* @param pmf
* PMF to compute the entropy.
* @return
* Entropy in bits of the given PMF.
*/
@PublicationReference(
author="Wikipedia",
title="Entropy (information theory)",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Entropy_(Information_theory)"
)
public static double getEntropy(
final ProbabilityMassFunction pmf )
{
// Compute the entropy by looping over the values in the maps
Collection domain = pmf.getDomain();
ArrayList data = new ArrayList( domain.size() );
for( DataType input : domain )
{
data.add( pmf.evaluate( input ) );
}
return UnivariateStatisticsUtil.computeEntropy(data);
}
/**
* Samples from the ProbabilityMassFunction. The return value will be
* sampled according to the given PMF.
* @param Type of data to use
* @param pmf PMF from which to sample
* @param random Random to sample from
* @param numSamples Number of samples to draw from the given PMF.
* @return
* Samples drawn according to the given PMF.
*/
public static ArrayList sample(
final ProbabilityMassFunction pmf,
final Random random,
final int numSamples )
{
ArrayList samples = new ArrayList(numSamples);
sampleInto(pmf, random, numSamples, samples);
return samples;
}
/**
* Samples from the ProbabilityMassFunction. The return value will be
* sampled according to the given PMF.
* @param Type of data to use
* @param pmf PMF from which to sample
* @param random Random to sample from
* @param numSamples Number of samples to draw from the given PMF.
* @param output Collection to add samples drawn according to the given PMF.
*/
public static void sampleInto(
final ProbabilityMassFunction pmf,
final Random random,
final int numSamples,
final Collection output)
{
if (numSamples == 1)
{
output.add(sampleSingle(pmf, random));
}
else if (numSamples > 1)
{
sampleMultipleInto(pmf, random, numSamples, output);
}
}
/**
* Draws a single sample from the given PMF
* @param
* Type of observations generated by the PMF
* @param pmf
* PMF from which to draw.
* @param random
* Random number generator
* @return
* Single sample from the PMF
*/
public static DataType sampleSingle(
final ProbabilityMassFunction pmf,
final Random random )
{
double p = random.nextDouble();
for( DataType x : pmf.getDomain() )
{
p -= pmf.evaluate(x);
if( p <= 0.0 )
{
return x;
}
}
return null;
}
/**
* Samples from the ProbabilityMassFunction. The return value will be
* sampled according to the given PMF.
* @param Type of data to use
* @param pmf PMF from which to sample
* @param random Random to sample from
* @param numSamples Number of samples to draw from the given PMF.
* @return
* Samples drawn according to the given PMF.
*/
@SuppressWarnings("unchecked")
public static ArrayList sampleMultiple(
final ProbabilityMassFunction pmf,
final Random random,
final int numSamples )
{
final ArrayList result = new ArrayList(numSamples);
sampleMultipleInto(pmf, random, numSamples, result);
return result;
}
/**
* Samples from the ProbabilityMassFunction. The return value will be
* sampled according to the given PMF.
* @param Type of data to use
* @param pmf PMF from which to sample
* @param random Random to sample from
* @param numSamples Number of samples to draw from the given PMF.
* @param output Collection to add samples drawn according to the given PMF.
*/
@SuppressWarnings("unchecked")
public static void sampleMultipleInto(
final ProbabilityMassFunction pmf,
final Random random,
final int numSamples,
final Collection output)
{
// Compute the cumulative probability counts.
// We can then use binary search to make the lookup process VERY zoomy.
int N = pmf.getDomain().size();
double[] cumulativeProbabilities = new double[ N ];
ArrayList domain =
CollectionUtil.asArrayList( pmf.getDomain() );
double psum = 0.0;
final int domainSize = domain.size();
for( int index = 0; index < domainSize; index++ )
{
final DataType x = domain.get(index);
psum += pmf.evaluate( x );
cumulativeProbabilities[index] = psum;
}
sampleMultipleInto(cumulativeProbabilities, domain, random, numSamples,
output);
}
/**
* Samples multiple elements from the domain proportionately to the
* cumulative weights in the given weight array using a fast
* binary search algorithm
* @param
* Type of data to be sampled
* @param cumulativeWeights
* Cumulative weights to sample from
* @param domain
* Domain from which to sample
* @param random
* Random number generator
* @param numSamples
* Number of samples to draw from the distribution
* @return
* Samples draw proportionately from the cumulative weights
*/
public static ArrayList sampleMultiple(
final double[] cumulativeWeights,
final List domain,
final Random random,
final int numSamples )
{
final ArrayList result = new ArrayList(numSamples);
sampleMultipleInto(cumulativeWeights, domain, random,
numSamples, result);
return result;
}
/**
* Samples multiple elements from the domain proportionately to the
* cumulative weights in the given weight array using a fast
* binary search algorithm
* @param
* Type of data to be sampled
* @param cumulativeWeights
* Cumulative weights to sample from
* @param domain
* Domain from which to sample
* @param random
* Random number generator
* @param numSamples
* Number of samples to draw from the distribution
* @param output
* The collection to put the samples in.
*/
public static void sampleMultipleInto(
final double[] cumulativeWeights,
final List domain,
final Random random,
final int numSamples,
final Collection output)
{
for( int n = 0; n < numSamples; n++ )
{
output.add(sample(cumulativeWeights, domain, random));
}
}
/**
* Samples an element from the domain proportionately to the
* cumulative weights in the given weight array using a fast
* binary search algorithm.
* @param
* Type of data to be sampled
* @param cumulativeWeights
* Cumulative weights to sample from
* @param domain
* Domain from which to sample
* @param random
* Random number generator
* @return
* A sample from the domain according to the weights.
*/
public static DataType sample(
final double[] cumulativeWeights,
final List domain,
final Random random)
{
final int index = DiscreteSamplingUtil.sampleIndexFromCumulativeProportions(
random, cumulativeWeights);
return domain.get(index);
}
/**
* Samples a single element from the domain proportionately to the given
* weights
* @param
* Type of data to be sampled
* @param weights
* Weights from which we will sample proportionately
* @param domain
* Domain from which to return the result
* @param random
* Random number generator
* @return
* A single sample from the domain proportionately from the weights
*/
public static DataType sampleSingle(
final double[] weights,
final Collection domain,
final Random random )
{
double sum = 0.0;
final int N = weights.length;
for( int n = 0; n < N; n++ )
{
sum += weights[n];
}
double s = sum * random.nextDouble();
int n = 0;
for( DataType value : domain )
{
s -= weights[n];
if( s <= 0.0 )
{
return value;
}
}
return null;
}
/**
* Inverts the discrete CDF, that is p=Pr{x<=X}.
* @param Type of number from the distribution
* @param cdf
* CDF of a discrete distribution.
* @param p
* Probability to invert, must be [0,1].
* @return
* Value of x such that p >= CDF(x) and p <= CDF(x_next).
*/
public static InputOutputPair inverse(
final CumulativeDistributionFunction cdf,
final double p )
{
ProbabilityUtil.assertIsProbability(p);
for( DataType x : ((DiscreteDistribution) cdf).getDomain() )
{
final double px = cdf.evaluate(x);
if( p <= px )
{
return new DefaultInputOutputPair( x, px );
}
}
throw new IllegalArgumentException(
"Could not invert CDF for p=" + p );
}
/**
* Computes the CDF value for the given PMF for the input. That is,
* the value of P=CDF(input)=sum(PMF(x<=input)).
* @param input
* Input to compute the CDF of.
* @param distribution
* Distribution to consider.
* @return
* CDF value of the distirbution for the given input
*/
public static double computeCumulativeValue(
final int input,
final ClosedFormDiscreteUnivariateDistribution distribution )
{
int minx = distribution.getMinSupport().intValue();
ProbabilityMassFunction pmf =
distribution.getProbabilityFunction();
double sum = 0.0;
for( int x = minx; x <= input; x++ )
{
sum += pmf.evaluate(x);
}
return sum;
}
}