/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
/*
* ChisqMixture.java
* Copyright (C) 2002 Yong Wang
*
*/
package weka.classifiers.functions.pace;
import java.util.Random;
import weka.core.Statistics;
/**
* Class for manipulating chi-square mixture distributions. <p>
*
* REFERENCES <p>
*
* Wang, Y. (2000). "A new approach to fitting linear models in high
* dimensional spaces." PhD Thesis. Department of Computer Science,
* University of Waikato, New Zealand. <p>
*
* Wang, Y. and Witten, I. H. (2002). "Modeling for optimal probability
* prediction." Proceedings of ICML'2002. Sydney. <p>
*
* @author Yong Wang (yongwang@cs.waikato.ac.nz)
* @version $Revision: 1.1.1.1 $ */
public class ChisqMixture extends MixtureDistribution
{
protected double separatingThreshold = 0.05;
protected double trimingThreshold = 0.5;
protected double supportThreshold = 0.5;
protected int maxNumSupportPoints = 200; // for computational reason
protected int fittingIntervalLength = 3;
protected double fittingIntervalThreshold = 0.5;
/** Contructs an empty ChisqMixture
*/
public ChisqMixture() {}
/** Gets the separating threshold value. This value is used by the method
separatable */
public double getSeparatingThreshold() {
return separatingThreshold;
}
/** Sets the separating threshold value
* @param t the threshold value
*/
public void setSeparatingThreshold( double t ) {
separatingThreshold = t;
}
/** Gets the triming thresholding value. This value is usef by the
method trim. */
public double getTrimingThreshold() {
return trimingThreshold;
}
/** Sets the triming thresholding value. */
public void setTrimingThreshold( double t ){
trimingThreshold = t;
}
/** Return true if a value can be considered for mixture estimatino
* separately from the data indexed between i0 and i1
* @param data the data supposedly generated from the mixture
* @param i0 the index of the first element in the group
* @param i1 the index of the last element in the group
* @param x the value
*/
public boolean separable( DoubleVector data, int i0, int i1, double x ) {
DoubleVector dataSqrt = data.sqrt();
double xh = Math.sqrt( x );
NormalMixture m = new NormalMixture();
m.setSeparatingThreshold( separatingThreshold );
return m.separable( dataSqrt, i0, i1, xh );
}
/** Contructs the set of support points for mixture estimation.
* @param data the data supposedly generated from the mixture
* @param ne the number of extra data that are suppposedly discarded
* earlier and not passed into here */
public DoubleVector supportPoints( DoubleVector data, int ne ) {
DoubleVector sp = new DoubleVector();
sp.setCapacity( data.size() + 1 );
if( data.get(0) < supportThreshold || ne != 0 )
sp.addElement( 0 );
for( int i = 0; i < data.size(); i++ )
if( data.get( i ) > supportThreshold )
sp.addElement( data.get(i) );
// The following will be fixed later???
if( sp.size() > maxNumSupportPoints )
throw new IllegalArgumentException( "Too many support points. " );
return sp;
}
/** Contructs the set of fitting intervals for mixture estimation.
* @param data the data supposedly generated from the mixture
*/
public PaceMatrix fittingIntervals( DoubleVector data ) {
PaceMatrix a = new PaceMatrix( data.size() * 2, 2 );
DoubleVector v = data.sqrt();
int count = 0;
double left, right;
for( int i = 0; i < data.size(); i++ ) {
left = v.get(i) - fittingIntervalLength;
if( left < fittingIntervalThreshold ) left = 0;
left = left * left;
right = data.get(i);
if( right < fittingIntervalThreshold )
right = fittingIntervalThreshold;
a.set( count, 0, left );
a.set( count, 1, right );
count++;
}
for( int i = 0; i < data.size(); i++ ) {
left = data.get(i);
if( left < fittingIntervalThreshold ) left = 0;
right = v.get(i) + fittingIntervalThreshold;
right = right * right;
a.set( count, 0, left );
a.set( count, 1, right );
count++;
}
a.setRowDimension( count );
return a;
}
/** Contructs the probability matrix for mixture estimation, given a set
* of support points and a set of intervals.
* @param s the set of support points
* @param intervals the intervals */
public PaceMatrix probabilityMatrix(DoubleVector s, PaceMatrix intervals) {
int ns = s.size();
int nr = intervals.getRowDimension();
PaceMatrix p = new PaceMatrix(nr, ns);
for( int i = 0; i < nr; i++ ) {
for( int j = 0; j < ns; j++ ) {
p.set( i, j,
Maths.pchisq( intervals.get(i, 1), s.get(j) ) -
Maths.pchisq( intervals.get(i, 0), s.get(j) ) );
}
}
return p;
}
/** Returns the pace6 estimate of a single value.
* @param x the value
*/
public double pace6 ( double x ) {
if( x > 100 ) return x; // pratical consideration. will modify later
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
DoubleVector mean = points.sqrt();
DoubleVector d = Maths.dchisqLog( x, points );
d.minusEquals( d.max() );
d = d.map("java.lang.Math", "exp").timesEquals( values );
double atilde = mean.innerProduct( d ) / d.sum();
return atilde * atilde;
}
/** Returns the pace6 estimate of a vector.
* @param x the vector
*/
public DoubleVector pace6( DoubleVector x ) {
DoubleVector pred = new DoubleVector( x.size() );
for(int i = 0; i < x.size(); i++ )
pred.set(i, pace6(x.get(i)) );
trim( pred );
return pred;
}
/** Returns the pace2 estimate of a vector.
* @param x the vector
*/
public DoubleVector pace2( DoubleVector x ) {
DoubleVector chf = new DoubleVector( x.size() );
for(int i = 0; i < x.size(); i++ ) chf.set( i, hf( x.get(i) ) );
chf.cumulateInPlace();
int index = chf.indexOfMax();
DoubleVector copy = x.copy();
if( index < x.size()-1 ) copy.set( index + 1, x.size()-1, 0 );
trim( copy );
return copy;
}
/** Returns the pace4 estimate of a vector.
* @param x the vector
*/
public DoubleVector pace4( DoubleVector x ) {
DoubleVector h = h( x );
DoubleVector copy = x.copy();
for( int i = 0; i < x.size(); i++ )
if( h.get(i) <= 0 ) copy.set(i, 0);
trim( copy );
return copy;
}
/** Trims the small values of the estaimte
* @param x the estimate vector */
public void trim( DoubleVector x ) {
for(int i = 0; i < x.size(); i++ ) {
if( x.get(i) <= trimingThreshold ) x.set(i, 0);
}
}
/**
* Computes the value of h(x) / f(x) given the mixture. The
* implementation avoided overflow.
* @param x the value */
public double hf( double AHat ) {
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
double x = Math.sqrt( AHat );
DoubleVector mean = points.sqrt();
DoubleVector d1 = Maths.dnormLog( x, mean, 1 );
double d1max = d1.max();
d1.minusEquals( d1max );
DoubleVector d2 = Maths.dnormLog( -x, mean, 1 );
d2.minusEquals( d1max );
d1 = d1.map("java.lang.Math", "exp");
d1.timesEquals( values );
d2 = d2.map("java.lang.Math", "exp");
d2.timesEquals( values );
return ( ( points.minus(x/2)).innerProduct( d1 ) -
( points.plus(x/2)).innerProduct( d2 ) )
/ (d1.sum() + d2.sum());
}
/**
* Computes the value of h(x) given the mixture.
* @param x the value */
public double h( double AHat ) {
if( AHat == 0.0 ) return 0.0;
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
double aHat = Math.sqrt( AHat );
DoubleVector aStar = points.sqrt();
DoubleVector d1 = Maths.dnorm( aHat, aStar, 1 ).timesEquals( values );
DoubleVector d2 = Maths.dnorm( -aHat, aStar, 1 ).timesEquals( values );
return points.minus(aHat/2).innerProduct( d1 ) -
points.plus(aHat/2).innerProduct( d2 );
}
/**
* Computes the value of h(x) given the mixture, where x is a vector.
* @param AHat the vector */
public DoubleVector h( DoubleVector AHat ) {
DoubleVector h = new DoubleVector( AHat.size() );
for( int i = 0; i < AHat.size(); i++ )
h.set( i, h( AHat.get(i) ) );
return h;
}
/**
* Computes the value of f(x) given the mixture.
* @param x the value */
public double f( double x ) {
DoubleVector points = mixingDistribution.getPointValues();
DoubleVector values = mixingDistribution.getFunctionValues();
return Maths.dchisq(x, points).timesEquals(values).sum();
}
/**
* Computes the value of f(x) given the mixture, where x is a vector.
* @param x the vector */
public DoubleVector f( DoubleVector x ) {
DoubleVector f = new DoubleVector( x.size() );
for( int i = 0; i < x.size(); i++ )
f.set( i, h( f.get(i) ) );
return f;
}
/** Converts to a string
*/
public String toString() {
return mixingDistribution.toString();
}
/** Method to test this class
*/
public static void main(String args[]) {
int n1 = 50;
int n2 = 50;
double ncp1 = 0;
double ncp2 = 10;
double mu1 = Math.sqrt( ncp1 );
double mu2 = Math.sqrt( ncp2 );
DoubleVector a = Maths.rnorm( n1, mu1, 1, new Random() );
a = a.cat( Maths.rnorm(n2, mu2, 1, new Random()) );
DoubleVector aNormal = a;
a = a.square();
a.sort();
DoubleVector means = (new DoubleVector( n1, mu1 )).cat(new DoubleVector(n2, mu2));
System.out.println("==========================================================");
System.out.println("This is to test the estimation of the mixing\n" +
"distribution of the mixture of non-central Chi-square\n" +
"distributions. The example mixture used is of the form: \n\n" +
" 0.5 * Chi^2_1(ncp1) + 0.5 * Chi^2_1(ncp2)\n" );
System.out.println("It also tests the PACE estimators. Quadratic losses of the\n" +
"estimators are given, measuring their performance.");
System.out.println("==========================================================");
System.out.println( "ncp1 = " + ncp1 + " ncp2 = " + ncp2 +"\n" );
System.out.println( a.size() + " observations are: \n\n" + a );
System.out.println( "\nQuadratic loss of the raw data (i.e., the MLE) = " +
aNormal.sum2( means ) );
System.out.println("==========================================================");
// find the mixing distribution
ChisqMixture d = new ChisqMixture();
d.fit( a, NNMMethod );
System.out.println( "The estimated mixing distribution is\n" + d );
DoubleVector pred = d.pace2( a.rev() ).rev();
System.out.println( "\nThe PACE2 Estimate = \n" + pred );
System.out.println( "Quadratic loss = " +
pred.sqrt().times(aNormal.sign()).sum2( means ) );
pred = d.pace4( a );
System.out.println( "\nThe PACE4 Estimate = \n" + pred );
System.out.println( "Quadratic loss = " +
pred.sqrt().times(aNormal.sign()).sum2( means ) );
pred = d.pace6( a );
System.out.println( "\nThe PACE6 Estimate = \n" + pred );
System.out.println( "Quadratic loss = " +
pred.sqrt().times(aNormal.sign()).sum2( means ) );
}
}