jgpml.covariancefunctions.CovSEard Maven / Gradle / Ivy
/* This file is part of the jgpml Project.
* http://github.com/renzodenardi/jgpml
*
* Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
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* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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package jgpml.covariancefunctions;
import Jama.Matrix;
import org.apache.commons.math3.util.FastMath;
import java.util.Arrays;
import static jgpml.covariancefunctions.MatrixOperations.exp;
/**
* Squared Exponential covariance function with Automatic Relevance Detemination (ARD) distance measure. The covariance
* function is parameterized as:
*
* k(x^p,x^q) = sf2 * exp(-(x^p - x^q)'*inv(P)*(x^p - x^q)/2)
*
* where the P matrix is diagonal with ARD parameters ell_1^2,...,ell_D^2, where D is the dimension of the input space
* and sf2 is the signal variance. The hyperparameters are:
*
* [ log(ell_1) log(ell_2) . log(ell_D) log(sqrt(sf2))]
*/
public class CovSEard implements CovarianceFunction {
private final int D;
private final int numParameters;
private Matrix K;
/**
* Creates a new CovSEard CovarianceFunction
*
* @param inputDimension muber of dimension of the input
*/
public CovSEard(int inputDimension) {
this.D = inputDimension;
this.numParameters = this.D + 1;
}
private static Matrix squareDist(Matrix a) {
return CovSEard.squareDist(a, a);
}
private static Matrix squareDist(Matrix a, Matrix b) {
Matrix C = new Matrix(a.getColumnDimension(), b.getColumnDimension());
int m = a.getColumnDimension();
int n = b.getColumnDimension();
int d = a.getRowDimension();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
double z = 0.0;
for (int k = 0; k < d; k++) {
double t = a.get(k, i) - b.get(k, j);
z += t * t;
}
C.set(i, j, z);
}
}
return C;
}
/**
* Returns the number of hyperparameters of CovSEard
*
* @return number of hyperparameters
*/
public int numParameters() {
return this.numParameters;
}
/**
* Compute covariance matrix of a dataset X
*
* @param loghyper column Matrix of hyperparameters
* @param X input dataset
* @return K covariance Matrix
*/
public Matrix compute(Matrix loghyper, Matrix X) {
if (X.getColumnDimension() != this.D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != this.numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + this.numParameters);
Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0)); // characteristic length scales
double sf2 = FastMath.exp(2 * loghyper.get(this.D, 0)); // signal variance
Matrix diag = new Matrix(this.D, this.D);
for (int i = 0; i < this.D; i++)
diag.set(i, i, 1 / ell.get(i, 0));
this.K = exp(CovSEard.squareDist(diag.times(X.transpose())).times(-0.5)).times(sf2); // SE covariance
return this.K;
}
/**
* Compute compute test set covariances
*
* @param loghyper column Matrix of hyperparameters
* @param X input dataset
* @param Xstar test set
* @return [K(Xstar, Xstar) K(X,Xstar)]
*/
public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
if (X.getColumnDimension() != this.D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != this.numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + this.numParameters);
Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0)); // characteristic length scales
double sf2 = FastMath.exp(2 * loghyper.get(this.D, 0)); // signal variance
double[] a = new double[Xstar.getRowDimension()];
Arrays.fill(a, sf2);
Matrix A = new Matrix(a, Xstar.getRowDimension());
Matrix diag = new Matrix(this.D, this.D);
for (int i = 0; i < this.D; i++)
diag.set(i, i, 1 / ell.get(i, 0));
Matrix B = exp(CovSEard.squareDist(diag.times(X.transpose()), diag.times(Xstar.transpose())).times(-0.5)).times(sf2);
return new Matrix[]{A, B};
}
/**
* Coompute the derivatives of this CovarianceFunction with respect to the hyperparameter with index
* idx
*
* @param loghyper hyperparameters
* @param X input dataset
* @param index hyperparameter index
* @return Matrix of derivatives
*/
public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
if (X.getColumnDimension() != this.D)
throw new IllegalArgumentException("The number of dimensions specified on the covariance function " + this.D + " must agree with the size of the input vector" + X.getColumnDimension());
if (loghyper.getColumnDimension() != 1 || loghyper.getRowDimension() != this.numParameters)
throw new IllegalArgumentException("Wrong number of hyperparameters, " + loghyper.getRowDimension() + " instead of " + this.numParameters);
if (index > numParameters() - 1)
throw new IllegalArgumentException("Wrong hyperparameters index " + index + " it should be smaller or equal to " + (numParameters() - 1));
Matrix A = null;
Matrix ell = exp(loghyper.getMatrix(0, this.D - 1, 0, 0)); // characteristic length scales
double sf2 = FastMath.exp(2 * loghyper.get(this.D, 0)); // signal variance
// noise variance
if (this.K.getRowDimension() != X.getRowDimension() || this.K.getColumnDimension() != X.getRowDimension()) {
Matrix diag = new Matrix(this.D, this.D);
for (int i = 0; i < this.D; i++)
diag.set(i, i, 1 / ell.get(i, 0));
this.K = exp(CovSEard.squareDist(diag.times(X.transpose())).times(-0.5)).times(sf2); // SE covariance
}
if (index < this.D) { //length scale parameters
Matrix col = CovSEard.squareDist(X.getMatrix(0, X.getRowDimension() - 1, index, index).transpose().times(1 / ell.get(index, 0)));
A = this.K.arrayTimes(col);
} else { // magnitude parameter
A = this.K.times(2);
this.K = null;
}
return A;
}
}