[1] | 1 | package agents.anac.y2015.Phoenix.GP;/* This file is part of the jgpml Project.
|
---|
| 2 | * http://github.com/renzodenardi/jgpml
|
---|
| 3 | *
|
---|
| 4 | * Copyright (c) 2011 Renzo De Nardi and Hugo Gravato-Marques
|
---|
| 5 | *
|
---|
| 6 | * Permission is hereby granted, free of charge, to any person
|
---|
| 7 | * obtaining a copy of this software and associated documentation
|
---|
| 8 | * files (the "Software"), to deal in the Software without
|
---|
| 9 | * restriction, including without limitation the rights to use,
|
---|
| 10 | * copy, modify, merge, publish, distribute, sublicense, and/or sell
|
---|
| 11 | * copies of the Software, and to permit persons to whom the
|
---|
| 12 | * Software is furnished to do so, subject to the following
|
---|
| 13 | * conditions:
|
---|
| 14 | *
|
---|
| 15 | * The above copyright notice and this permission notice shall be
|
---|
| 16 | * included in all copies or substantial portions of the Software.
|
---|
| 17 | *
|
---|
| 18 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
---|
| 19 | * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
---|
| 20 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
---|
| 21 | * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
---|
| 22 | * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
---|
| 23 | * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
---|
| 24 | * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
---|
| 25 | * OTHER DEALINGS IN THE SOFTWARE.
|
---|
| 26 | */
|
---|
| 27 |
|
---|
| 28 | import static agents.anac.y2015.Phoenix.GP.MatrixOperations.*;
|
---|
| 29 |
|
---|
| 30 | import agents.Jama.Matrix;
|
---|
| 31 |
|
---|
| 32 | /** Linear covariance function with a single hyperparameter. The covariance
|
---|
| 33 | * function is parameterized as:
|
---|
| 34 | * <p>
|
---|
| 35 | * k(x^p,x^q) = x^p'*inv(P)*x^q + 1./t2;
|
---|
| 36 | * <p>
|
---|
| 37 | * where the P matrix is t2 times the unit matrix. The second term plays the
|
---|
| 38 | * role of the bias. The hyperparameter is:
|
---|
| 39 | * <p>
|
---|
| 40 | * [ log(sqrt(t2)) ]
|
---|
| 41 | */
|
---|
| 42 |
|
---|
| 43 | public class CovLINone implements CovarianceFunction{
|
---|
| 44 |
|
---|
| 45 | public CovLINone(){}
|
---|
| 46 |
|
---|
| 47 | /**
|
---|
| 48 | * Returns the number of hyperparameters of this<code>PhoenixAlpha.CovarianceFunction</code>
|
---|
| 49 | *
|
---|
| 50 | * @return number of hyperparameters
|
---|
| 51 | */
|
---|
| 52 | public int numParameters() {
|
---|
| 53 | return 1;
|
---|
| 54 | }
|
---|
| 55 |
|
---|
| 56 | /**
|
---|
| 57 | * Compute covariance matrix of a dataset X
|
---|
| 58 | *
|
---|
| 59 | * @param loghyper column <code>Matrix</code> of hyperparameters
|
---|
| 60 | * @param X input dataset
|
---|
| 61 | * @return K covariance <code>Matrix</code>
|
---|
| 62 | */
|
---|
| 63 | public Matrix compute(Matrix loghyper, Matrix X) {
|
---|
| 64 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
|
---|
| 65 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
|
---|
| 66 |
|
---|
| 67 | final double it2 = Math.exp(-2*loghyper.get(0,0));
|
---|
| 68 |
|
---|
| 69 | Matrix A = X.times(X.transpose());
|
---|
| 70 | return addValue(A,1).times(it2);
|
---|
| 71 | }
|
---|
| 72 |
|
---|
| 73 | /**
|
---|
| 74 | * Compute compute test set covariances
|
---|
| 75 | *
|
---|
| 76 | * @param loghyper column <code>Matrix</code> of hyperparameters
|
---|
| 77 | * @param X input dataset
|
---|
| 78 | * @param Xstar test set
|
---|
| 79 | * @return [K(Xstar,Xstar) K(X,Xstar)]
|
---|
| 80 | */
|
---|
| 81 | public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
|
---|
| 82 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
|
---|
| 83 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
|
---|
| 84 |
|
---|
| 85 | final double it2 = Math.exp(-2*loghyper.get(0,0));
|
---|
| 86 |
|
---|
| 87 | Matrix A = sumRows(Xstar.arrayTimes(Xstar));
|
---|
| 88 |
|
---|
| 89 | A= addValue(A,1).times(it2);
|
---|
| 90 |
|
---|
| 91 | Matrix B = X.times(Xstar.transpose());
|
---|
| 92 | B = addValue(B,1).times(it2);
|
---|
| 93 |
|
---|
| 94 | return new Matrix[]{A,B};
|
---|
| 95 | }
|
---|
| 96 |
|
---|
| 97 | /**
|
---|
| 98 | * Coompute the derivatives of this <code>PhoenixAlpha.CovarianceFunction</code> with respect
|
---|
| 99 | * to the hyperparameter with index <code>idx</code>
|
---|
| 100 | *
|
---|
| 101 | * @param loghyper hyperparameters
|
---|
| 102 | * @param X input dataset
|
---|
| 103 | * @param index hyperparameter index
|
---|
| 104 | * @return <code>Matrix</code> of derivatives
|
---|
| 105 | */
|
---|
| 106 | public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
|
---|
| 107 |
|
---|
| 108 | if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
|
---|
| 109 | throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
|
---|
| 110 | if(index>numParameters()-1)
|
---|
| 111 | throw new IllegalArgumentException("Wrong hyperparameters index "+index+" it should be smaller or equal to "+(numParameters()-1));
|
---|
| 112 |
|
---|
| 113 | final double it2 = Math.exp(-2*loghyper.get(0,0));
|
---|
| 114 | Matrix A = X.times(X.transpose());
|
---|
| 115 | return addValue(A,1).times(-2*it2);
|
---|
| 116 | }
|
---|
| 117 |
|
---|
| 118 | public static void main(String[] args) {
|
---|
| 119 | CovLINone cf = new CovLINone();
|
---|
| 120 |
|
---|
| 121 | Matrix X = Matrix.identity(6,6);
|
---|
| 122 | Matrix logtheta = new Matrix(new double[][]{{0.1}});
|
---|
| 123 |
|
---|
| 124 | Matrix z = new Matrix(new double[][]{{1,2,3,4,5,6},{1,2,3,4,5,6}});
|
---|
| 125 |
|
---|
| 126 | System.out.println("");
|
---|
| 127 | Matrix K = cf.compute(logtheta,X);
|
---|
| 128 | K.print(K.getColumnDimension(), 8);
|
---|
| 129 |
|
---|
| 130 | Matrix[] res = cf.compute(logtheta,X,z);
|
---|
| 131 |
|
---|
| 132 | res[0].print(res[0].getColumnDimension(), 8);
|
---|
| 133 | res[1].print(res[1].getColumnDimension(), 8);
|
---|
| 134 |
|
---|
| 135 | Matrix d = cf.computeDerivatives(logtheta,X,0);
|
---|
| 136 |
|
---|
| 137 | d.print(d.getColumnDimension(), 8);
|
---|
| 138 |
|
---|
| 139 | }
|
---|
| 140 | }
|
---|