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/*
* File: LaplaceDistribution.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Jul 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.distribution;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.NumberAverager;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution;
import gov.sandia.cognition.statistics.DistributionEstimator;
import gov.sandia.cognition.statistics.DistributionWeightedEstimator;
import gov.sandia.cognition.statistics.EstimableDistribution;
import gov.sandia.cognition.statistics.InvertibleCumulativeDistributionFunction;
import gov.sandia.cognition.statistics.UnivariateProbabilityDensityFunction;
import gov.sandia.cognition.statistics.SmoothCumulativeDistributionFunction;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.WeightedValue;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Random;
/**
* A Laplace distribution, sometimes called a double exponential distribution.
* This distribution arrises when evaluating the difference between two iid
* exponential random variables, or when sampling Brownian motion at
* exponentially distributed time steps.
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReference(
author="Wikipedia",
title="Laplace distribution",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Laplace_distribution"
)
public class LaplaceDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution
{
/**
* Default mean, {@value}.
*/
public static final double DEFAULT_MEAN = 0.0;
/**
* Default scale, {@value}.
*/
public static final double DEFAULT_SCALE = 1.0;
/**
* Mean of the distribution
*/
protected double mean;
/**
* Scale factor of the distribution, must be greater than zero.
*/
protected double scale;
/**
* Creates a new instance of LaplaceDistribution
*/
public LaplaceDistribution()
{
this( DEFAULT_MEAN, DEFAULT_SCALE );
}
/**
* Creates a new instance of LaplaceDistribution
* @param mean
* Mean of the distribution
* @param scale
* Scale factor of the distribution, must be greater than zero.
*/
public LaplaceDistribution(
final double mean,
final double scale )
{
super();
this.setMean(mean);
this.setScale(scale);
}
/**
* Copy Constructor
* @param other LaplaceDistribution to copy
*/
public LaplaceDistribution(
final LaplaceDistribution other )
{
this( other.getMean(), other.getScale() );
}
@Override
public LaplaceDistribution clone()
{
return (LaplaceDistribution) super.clone();
}
@Override
public Double getMean()
{
return this.mean;
}
@Override
public double getMeanAsDouble()
{
return this.mean;
}
/**
* Setter for mean
* @param mean
* Mean of the distribution
*/
public void setMean(
final double mean)
{
this.mean = mean;
}
/**
* Getter for scale
* @return
* Scale factor of the distribution, must be greater than zero.
*/
public double getScale()
{
return this.scale;
}
/**
* Setter for scale
* @param scale
* Scale factor of the distribution, must be greater than zero.
*/
public void setScale(
final double scale)
{
if( scale <= 0.0 )
{
throw new IllegalArgumentException( "scale must be > 0.0" );
}
this.scale = scale;
}
@Override
public double sampleAsDouble(
final Random random)
{
final double p = random.nextDouble();
return LaplaceDistribution.CDF.inverse(this, p);
}
@Override
public void sampleInto(
final Random random,
final double[] output,
final int start,
final int length)
{
final int end = start + length;
for (int i = start; i < end; i++)
{
output[i] = this.sampleAsDouble(random);
}
}
@Override
public Vector convertToVector()
{
return VectorFactory.getDefault().copyValues(
this.getMean(), this.getScale() );
}
@Override
public void convertFromVector(
final Vector parameters)
{
parameters.assertDimensionalityEquals(2);
this.setMean( parameters.getElement(0) );
this.setScale( parameters.getElement(1) );
}
@Override
public double getVariance()
{
final double b = this.getScale();
return 2.0*b*b;
}
@Override
public String toString()
{
return "Mean: " + this.getMean() + ", Scale: " + this.getScale();
}
@Override
public LaplaceDistribution.CDF getCDF()
{
return new LaplaceDistribution.CDF( this );
}
@Override
public LaplaceDistribution.PDF getProbabilityFunction()
{
return new LaplaceDistribution.PDF( this );
}
@Override
public Double getMinSupport()
{
return Double.NEGATIVE_INFINITY;
}
@Override
public Double getMaxSupport()
{
return Double.POSITIVE_INFINITY;
}
@Override
public LaplaceDistribution.MaximumLikelihoodEstimator getEstimator()
{
return new LaplaceDistribution.MaximumLikelihoodEstimator();
}
/**
* CDF of the Laplace distribution.
*/
public static class CDF
extends LaplaceDistribution
implements SmoothCumulativeDistributionFunction,
InvertibleCumulativeDistributionFunction
{
/**
* Creates a new instance of LaplaceDistribution.CDF
*/
public CDF()
{
super();
}
/**
* Creates a new instance of LaplaceDistribution.CDF
* @param mean
* Mean of the distribution
* @param scale
* Scale factor of the distribution, must be greater than zero.
*/
public CDF(
final double mean,
final double scale )
{
super(mean,scale);
}
/**
* Copy Constructor
* @param other LaplaceDistribution to copy
*/
public CDF(
final LaplaceDistribution other )
{
super( other );
}
@Override
public Double evaluate(
final Double input)
{
return this.evaluate(input.doubleValue());
}
@Override
public double evaluateAsDouble(
final Double input)
{
return this.evaluate(input.doubleValue());
}
@Override
public double evaluate(
final double input)
{
if( input == Double.NEGATIVE_INFINITY )
{
return 0.0;
}
else if( input == Double.POSITIVE_INFINITY )
{
return 1.0;
}
double delta = input - this.mean;
return 0.5 * (1.0 + Math.signum(delta)*(1.0-Math.exp(-Math.abs(delta)/this.scale)));
}
/**
* Computes the inverse of the CDF for the give probability. That is,
* find x=CDF.inverse(p) so that CDF(x)=p.
* @param p
* Probability to invert, must be [0,1].
* @return
* Finds the value of the CDF "x" so that CDF(x)=p.
*/
@Override
public Double inverse(
final double p )
{
return inverse( this, p );
}
/**
* Computes the inverse of the CDF for the give probability. That is,
* find x=CDF.inverse(p) so that CDF(x)=p.
* @param laplace
* Laplace distribution to invert.
* @param p
* Probability to invert, must be [0,1].
* @return
* Finds the value of the CDF "x" so that CDF(x)=p.
*/
public static double inverse(
final LaplaceDistribution laplace,
final double p )
{
if( p <= 0.0 )
{
return laplace.getMinSupport();
}
else if( p >= 1.0 )
{
return laplace.getMaxSupport();
}
else
{
double delta = p - 0.5;
return laplace.mean -
laplace.scale*Math.signum(delta)*Math.log(1.0-2.0*Math.abs(delta));
}
}
@Override
public LaplaceDistribution.CDF getCDF()
{
return this;
}
@Override
public LaplaceDistribution.PDF getDerivative()
{
return this.getProbabilityFunction();
}
@Override
public Double differentiate(
final Double input)
{
return this.getDerivative().evaluate(input);
}
}
/**
* The PDF of a Laplace Distribution.
*/
public static class PDF
extends LaplaceDistribution
implements UnivariateProbabilityDensityFunction
{
/**
* Creates a new instance of LaplaceDistribution.PDF
*/
public PDF()
{
super();
}
/**
* Creates a new instance of LaplaceDistribution.PDF
* @param mean
* Mean of the distribution
* @param scale
* Scale factor of the distribution, must be greater than zero.
*/
public PDF(
final double mean,
final double scale )
{
super(mean,scale);
}
/**
* Copy Constructor
* @param other LaplaceDistribution to copy
*/
public PDF(
final LaplaceDistribution other )
{
super( other );
}
@Override
public double evaluate(
final double input)
{
double front = 0.5 / this.scale;
double exponent = -Math.abs(input-this.mean) / this.scale;
return front * Math.exp(exponent);
}
@Override
public Double evaluate(
Double input)
{
return this.evaluate( input.doubleValue() );
}
@Override
public double evaluateAsDouble(
final Double input)
{
return this.evaluate(input.doubleValue());
}
@Override
public double logEvaluate(
final Double input)
{
return this.logEvaluate((double) input);
}
@Override
public double logEvaluate(
final double input)
{
final double n1 = Math.log( 0.5 / this.scale );
final double n2 = -Math.abs(input-this.mean) / this.scale;
return n1 + n2;
}
@Override
public LaplaceDistribution.PDF getProbabilityFunction()
{
return this;
}
}
/**
* Estimates the ML parameters of a Laplace distribution from a
* Collection of Numbers.
*/
public static class MaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionEstimator
{
/**
* Default constructor
*/
public MaximumLikelihoodEstimator()
{
super();
}
@Override
public LaplaceDistribution learn(
final Collection data)
{
final double mean = NumberAverager.INSTANCE.summarize(data);
double absSum = 0.0;
for( Double value : data )
{
double delta = value - mean;
absSum += Math.abs(delta);
}
double scale = absSum / data.size();
return new LaplaceDistribution( mean, scale );
}
}
/**
* Creates a UnivariateGaussian from weighted data
*/
public static class WeightedMaximumLikelihoodEstimator
extends AbstractCloneableSerializable
implements DistributionWeightedEstimator
{
/**
* Default constructor
*/
public WeightedMaximumLikelihoodEstimator()
{
super();
}
/**
* Creates a new instance of LaplaceDistribution using a weighted
* Maximum Likelihood estimate based on the given data
* @param data
* Weighed pairs of data (first is data, second is weight) that was
* generated by some unknown LaplaceDistribution distribution
* @return
* Maximum Likelihood UnivariateGaussian that generated the data
*/
@Override
public LaplaceDistribution learn(
final Collection> data )
{
double mean = 0.0;
double weightSum = 0.0;
for( WeightedValue weightedValue : data )
{
double weight = weightedValue.getWeight();
if( weight != 0.0 )
{
double value = weightedValue.getValue().doubleValue();
mean += weight*value;
weightSum += weight;
}
}
if( weightSum != 0.0 )
{
mean /= weightSum;
}
// Now compute the shape factor
double shape = 0.0;
for( WeightedValue weightedValue : data )
{
double weight = weightedValue.getWeight();
if( weight != 0.0 )
{
double value = weightedValue.getValue().doubleValue();
double delta = value - mean;
shape += weight * Math.abs(delta);
}
}
if( weightSum != 0.0 )
{
shape /= weightSum;
}
return new LaplaceDistribution( mean, shape );
}
}
}