source: src/main/java/agents/anac/y2015/Phoenix/GP/CovNNoneNoise.java@ 346

Last change on this file since 346 was 1, checked in by Wouter Pasman, 6 years ago

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1package 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
28import agents.Jama.Matrix;
29
30/**
31 * Neural network covariance function with a single parameter for the distance
32 * measure and white noise. The covariance function is parameterized as:
33 * <P>
34 * k(x^p,x^q) = sf2 * asin(x^p'*P*x^q / sqrt[(1+x^p'*P*x^p)*(1+x^q'*P*x^q)]) + s2 * \delta(p,q)
35 * <P>
36 * where the x^p and x^q vectors on the right hand side have an added extra bias
37 * entry with unit value. P is ell^-2 times the unit matrix and sf2 controls the
38 * signal variance. The hyperparameters are:
39 * <P>
40 * [ log(ell)
41 * log(sqrt(sf2)
42 * log(s2)]
43 *
44 * <P>
45 * For reson of speed consider to use this covariance function instead of <code>PhoenixAlpha.CovSum(PhoenixAlpha.CovNNone,PhoenixAlpha.CovNoise)</code>
46 *
47 */
48
49public class CovNNoneNoise implements CovarianceFunction{
50
51 double[][] k;
52 double[][] q;
53
54 public CovNNoneNoise(){}
55
56
57 /**
58 * Returns the number of hyperparameters of this<code>PhoenixAlpha.CovarianceFunction</code>
59 *
60 * @return number of hyperparameters
61 */
62 public int numParameters() {
63 return 3;
64 }
65
66 /**
67 * Compute covariance matrix of a dataset X
68 *
69 * @param loghyper column <code>Matrix</code> of hyperparameters
70 * @param X input dataset
71 * @return K covariance <code>Matrix</code>
72 */
73 public Matrix compute(Matrix loghyper, Matrix X) {
74
75 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
76 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
77
78 final double ell = Math.exp(loghyper.get(0,0));
79 final double em2 = 1/(ell*ell);
80 final double oneplusem2 = 1+em2;
81 final double sf2 = Math.exp(2*loghyper.get(1,0));
82 final double s2 = Math.exp(2*loghyper.get(2,0));
83
84 final int m = X.getRowDimension();
85 final int n = X.getColumnDimension();
86 double[][] x= X.getArray();
87
88// Matrix Xc= X.times(1/ell);
89//
90// Q = Xc.times(Xc.transpose());
91// System.out.print("Q=");Q.print(Q.getColumnDimension(), 8);
92
93// Q = new Matrix(m,m);
94// double[][] q = Q.getArray();
95// double[][] q;
96 q = new double[m][m];
97
98 for(int i=0;i<m;i++){
99 for(int j=0;j<m;j++){
100 double t = 0;
101 for(int k=0;k<n;k++){
102 t+=x[i][k]*x[j][k]*em2;
103 }
104 q[i][j]=t;
105 }
106 }
107// System.out.print("q=");Q.print(Q.getColumnDimension(), 8);
108
109// Matrix dQ = diag(Q);
110// Matrix dQT = dQ.transpose();
111// Matrix Qc = Q.copy();
112// K = addValue(Qc,em2).arrayRightDivide(sqrt(addValue(dQ,1+em2)).times(sqrt(addValue(dQT,1+em2))));
113// System.out.print("K=");K.print(K.getColumnDimension(), 8);
114
115 double[] dq = new double[m];
116 for(int i=0;i<m;i++){
117 dq[i]=Math.sqrt(oneplusem2+q[i][i]);
118 }
119
120 //K = new Matrix(m,m);
121 Matrix A = new Matrix(m,m);
122 //double[][] k;
123 k = new double[m][m];//K.getArray();
124 double[][] a =A.getArray();
125 for(int i=0;i<m;i++){
126 final double dqi = dq[i];
127 for(int j=0;j<m;j++){
128 final double t = (em2+q[i][j])/(dqi*dq[j]);
129 k[i][j]=t;
130 a[i][j]=sf2*Math.asin(t);
131 }
132 a[i][i]+=s2;
133 }
134// System.out.print("k=");K.print(K.getColumnDimension(), 8);
135// System.out.println("");
136
137// Matrix A = asin(K).times(sf2);
138 return A;
139 }
140
141 /**
142 * Compute compute test set covariances
143 *
144 * @param loghyper column <code>Matrix</code> of hyperparameters
145 * @param X input dataset
146 * @param Xstar test set
147 * @return [K(Xstar,Xstar) K(X,Xstar)]
148 */
149 public Matrix[] compute(Matrix loghyper, Matrix X, Matrix Xstar) {
150
151 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
152 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
153
154 final double ell = Math.exp(loghyper.get(0,0));
155 final double em2 = 1/(ell*ell);
156 final double oneplusem2 = 1+em2;
157 final double sf2 = Math.exp(2*loghyper.get(1,0));
158 final double s2 = Math.exp(2*loghyper.get(2,0));
159
160
161 final int m = X.getRowDimension();
162 final int n = X.getColumnDimension();
163 double[][] x= X.getArray();
164 final int mstar = Xstar.getRowDimension();
165 final int nstar = Xstar.getColumnDimension();
166 double[][] xstar= Xstar.getArray();
167
168
169 double[] sumxstardotTimesxstar = new double[mstar];
170 for(int i=0; i<mstar; i++){
171 double t =0;
172 for(int j=0; j<nstar; j++){
173 final double tt = xstar[i][j];
174 t+=tt*tt*em2;
175 }
176 sumxstardotTimesxstar[i]=t;
177 }
178
179 Matrix A = new Matrix(mstar,1);
180 double[][] a = A.getArray();
181 for(int i=0; i<mstar; i++){
182 a[i][0]=sf2*Math.asin((em2+sumxstardotTimesxstar[i])/(oneplusem2+sumxstardotTimesxstar[i]))+s2;
183 }
184
185
186
187// X = X.times(1/ell);
188// Xstar = Xstar.times(1/ell);
189// Matrix tmp = sumRows(Xstar.arrayTimes(Xstar));
190//
191// Matrix tmp2 = tmp.copy();
192// addValue(tmp,em2);
193// addValue(tmp2,oneplusem2);
194// Matrix A = asin(tmp.arrayRightDivide(tmp2)).times(sf2);
195
196
197 double[] sumxdotTimesx = new double[m];
198 for(int i=0; i<m; i++){
199 double t =0;
200 for(int j=0; j<n; j++){
201 final double tt = x[i][j];
202 t+=tt*tt*em2;
203 }
204 sumxdotTimesx[i]=t+oneplusem2;
205 }
206
207 Matrix B = new Matrix(m,mstar);
208 double[][] b = B.getArray();
209 for(int i=0; i<m; i++){
210 final double[] xi = x[i];
211 for(int j=0; j<mstar; j++){
212 double t=0;
213 final double[] xstarj = xstar[j];
214 for(int k=0; k<n; k++){
215 t+=xi[k]*xstarj[k]*em2;
216 }
217 b[i][j]=t+em2;
218 }
219 }
220
221 for(int i=0; i<m; i++){
222 for(int j=0; j<mstar; j++){
223 b[i][j] = sf2*Math.asin(b[i][j]/Math.sqrt((sumxstardotTimesxstar[j]+oneplusem2)*sumxdotTimesx[i]));
224 }
225 }
226
227
228
229// tmp = sumRows(X.arrayTimes(X));
230// addValue(tmp,oneplusem2);
231//
232// tmp2=tmp2.transpose();
233//
234// tmp = addValue(X.times(Xstar.transpose()),em2).arrayRightDivide(sqrt(tmp.times(tmp2)));
235// Matrix B = asin(tmp).times(sf2);
236
237 //System.out.println("");
238 return new Matrix[]{A,B};
239 }
240
241 /**
242 * Coompute the derivatives of this <code>PhoenixAlpha.CovarianceFunction</code> with respect
243 * to the hyperparameter with index <code>idx</code>
244 *
245 * @param loghyper hyperparameters
246 * @param X input dataset
247 * @param index hyperparameter index
248 * @return <code>Matrix</code> of derivatives
249 */
250 public Matrix computeDerivatives(Matrix loghyper, Matrix X, int index) {
251
252 if(loghyper.getColumnDimension()!=1 || loghyper.getRowDimension()!=numParameters())
253 throw new IllegalArgumentException("Wrong number of hyperparameters, "+loghyper.getRowDimension()+" instead of "+numParameters());
254 if(index>numParameters()-1)
255 throw new IllegalArgumentException("Wrong hyperparameters index "+index+" it should be smaller or equal to "+(numParameters()-1));
256
257 final double ell = Math.exp(loghyper.get(0,0));
258 final double em2 = 1/(ell*ell);
259 final double oneplusem2 = 1+em2;
260 final double twosf2 = 2*Math.exp(2*loghyper.get(1,0));
261 final double twos2 = 2*Math.exp(2*loghyper.get(2,0));
262
263 final int m = X.getRowDimension();
264 final int n = X.getColumnDimension();
265 double[][] x= X.getArray();
266
267// Matrix X = XX.times(1/ell);
268// double[][] q=null;
269 if(q==null || q.length!=m || q[0].length!=m) {
270 q = new double[m][m];
271
272 for(int i=0;i<m;i++){
273 for(int j=0;j<m;j++){
274 double t = 0;
275 for(int k=0;k<n;k++){
276 t+=x[i][k]*x[j][k]*em2;
277 }
278 q[i][j]=t;
279 }
280 }
281 }
282
283 double[] dq = new double[m];
284 for(int i=0;i<m;i++){
285 dq[i]=Math.sqrt(oneplusem2+q[i][i]);
286 }
287// double[][] k=null;
288 if(k==null || k.length!=m || k[0].length!=m) {
289 k = new double[m][m];
290 for(int i=0;i<m;i++){
291 final double dqi = dq[i];
292 for(int j=0;j<m;j++){
293 final double t = (em2+q[i][j])/(dqi*dq[j]);
294 k[i][j]=t;
295 }
296 }
297 }
298
299// Matrix Xc= XX.times(1/ell);
300// Matrix Q = Xc.times(Xc.transpose());
301//
302// Matrix dQ = diag(Q);
303// Matrix dQT = dQ.transpose();
304// Matrix K = addValue(Q.copy(),em2).arrayRightDivide(sqrt(addValue(dQ.copy(),1+em2)).times(sqrt(addValue(dQT,1+em2))));
305// Matrix dQc = dQ.copy();
306
307 Matrix A = null;
308 switch(index){
309 case 0:
310 for(int i=0;i<m;i++){
311 dq[i]=oneplusem2+q[i][i];
312 }
313 double[] v = new double[m];
314 for(int i=0; i<m; i++){
315 double t =0;
316 for(int j=0; j<n; j++){
317 final double xij = x[i][j];
318 t+=xij*xij*em2;
319 }
320 v[i]=(t+em2)/(dq[i]);
321 }
322
323// Matrix test = addValue(sumRows(X.arrayTimes(X)),em2);
324// Matrix tmp = addValue(dQc,1+em2);
325// Matrix V = addValue(sumRows(X.arrayTimes(X)),em2).arrayRightDivide(tmp);
326//
327// tmp = sqrt(tmp);
328// tmp = addValue(Q.copy(),em2).arrayRightDivide(tmp.times(tmp.transpose()));
329
330 for(int i=0; i<m; i++){
331 final double vi = v[i];
332 for(int j=0; j<m; j++){
333 double t =(q[i][j]+em2)/(Math.sqrt(dq[i])*Math.sqrt(dq[j]));
334 final double kij = k[i][j];
335 q[i][j]=-twosf2*((t-(0.5*kij*(vi+v[j])))/Math.sqrt(1-kij*kij));
336 }
337 }
338
339// Matrix tmp2 = new Matrix(m,m);
340// for(int j=0; j<m; j++)
341// tmp2.setMatrix(0,m-1,j,j,V);
342//
343// tmp = tmp.minus(K.arrayTimes(tmp2.plus(tmp2.transpose())).times(0.5));
344//
345// A = tmp.arrayRightDivide(sqrtOneMinusSqr(K)).times(-twosf2);
346
347 A = new Matrix(q);
348// System.out.println("");
349 q=null;
350 break;
351 case 1:
352 for(int i=0; i<m; i++){
353 for(int j=0; j<m; j++){
354 k[i][j]=Math.asin(k[i][j])*twosf2;
355 }
356 }
357// A = asin(K).times(twosf2);
358// K=null;
359 A = new Matrix(k);
360 k=null;
361
362 break;
363
364 case 2:
365 double[][] a = new double[m][m];
366 for(int i=0; i<m;i++) a[i][i]=twos2;
367
368 A = new Matrix(a);
369
370 break;
371 default:
372 throw new IllegalArgumentException("the covariance function PhoenixAlpha.CovNNoneNoise alllows for a maximum of 3 parameters!!");
373 }
374 return A;
375 }
376
377// private static Matrix sqrtOneMinusSqr(Matrix in){
378// Matrix out = new Matrix(in.getRowDimension(),in.getColumnDimension());
379// for(int i=0; i<in.getRowDimension(); i++)
380// for(int j=0; j<in.getColumnDimension(); j++) {
381// final double tmp = in.get(i,j);
382// out.set(i,j,Math.sqrt(1-tmp*tmp));
383// }
384// return out;
385// }
386
387 public static void main(String[] args) {
388
389 CovarianceFunction cf = new CovNNoneNoise();
390 CovarianceFunction cf2 = new CovSum(6,new CovNNone(), new CovNoise());
391
392
393 Matrix X = Matrix.identity(10,6);
394
395 for(int i=0; i<X.getRowDimension(); i++)
396 for(int j=0; j<X.getColumnDimension(); j++)
397 X.set(i,j,Math.random());
398
399 Matrix logtheta = new Matrix(new double[][]{{0.1},{0.2},{Math.log(0.1)}});
400
401 Matrix z =new Matrix(new double[][]{{1,2,3,4,5,6},{1,2,3,4,5,6}});
402
403// long start = System.currentTimeMillis();
404// Matrix K = cf.compute(logtheta,X);
405// K.print(K.getColumnDimension(), 15);
406
407// long stop = System.currentTimeMillis();
408// System.out.println(""+(stop-start));
409//
410// start = System.currentTimeMillis();
411// K = cf2.compute(logtheta,X);
412// K.print(K.getColumnDimension(), 15);
413// stop = System.currentTimeMillis();
414// System.out.println(""+(stop-start));
415
416
417
418// long start = System.currentTimeMillis();
419// Matrix[] res = cf.compute(logtheta,X,z);
420// res[0].print(res[0].getColumnDimension(), 8);
421// res[1].print(res[1].getColumnDimension(), 8);
422
423// long stop = System.currentTimeMillis();
424// System.out.println(""+(stop-start));
425
426
427
428// res = cf2.compute(logtheta,X,z);
429// res[0].print(res[0].getColumnDimension(), 8);
430// res[1].print(res[1].getColumnDimension(), 8);
431
432// long stop = System.currentTimeMillis();
433// System.out.println(""+(stop-start));
434
435
436
437
438// Matrix d = cf.computeDerivatives(logtheta,X,0);
439// d.print(d.getColumnDimension(), 8);
440
441 //d = cf2.computeDerivatives(logtheta,X,0);
442 //d.print(d.getColumnDimension(), 8);
443
444
445 }
446}
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