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finished a.EMGLLF.c [to test] ; fix indices in EMGLLF.c [by cols]
[valse.git] / src / sources / EMGLLF.c
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BA		 1#include "EMGLLF.h"
2#include <gsl/gsl_linalg.h>
3
4cab944a 4// TODO: don't recompute indexes every time......
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BA		 5void EMGLLF(
6 // IN parameters
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BA		 7 const double* phiInit, // parametre initial de moyenne renormalisé
8 const double* rhoInit, // parametre initial de variance renormalisé
9 const double* piInit, // parametre initial des proportions
10 const double* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
11 int mini, // nombre minimal d'itérations dans l'algorithme EM
12 int maxi, // nombre maximal d'itérations dans l'algorithme EM
13 double gamma, // valeur de gamma : puissance des proportions dans la pénalisation pour un Lasso adaptatif
14 double lambda, // valeur du paramètre de régularisation du Lasso
15 const double* X, // régresseurs
16 const double* Y, // réponse
17 double tau, // seuil pour accepter la convergence
1d3c1faa 18 // OUT parameters (all pointers, to be modified)
4cab944a
BA		 19 double* phi, // parametre de moyenne renormalisé, calculé par l'EM
20 double* rho, // parametre de variance renormalisé, calculé par l'EM
21 double* pi, // parametre des proportions renormalisé, calculé par l'EM
22 double* LLF, // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
23 double* S,
1d3c1faa 24 // additional size parameters
4cab944a
BA		 25 int n, // nombre d'echantillons
26 int p, // nombre de covariables
27 int m, // taille de Y (multivarié)
28 int k) // nombre de composantes dans le mélange
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BA		 29{
30 //Initialize outputs
31 copyArray(phiInit, phi, p*m*k);
32 copyArray(rhoInit, rho, m*m*k);
33 copyArray(piInit, pi, k);
34 zeroArray(LLF, maxi);
35 //S is already allocated, and doesn't need to be 'zeroed'
4cab944a 36
1d3c1faa
BA		 37 //Other local variables
38 //NOTE: variables order is always [maxi],n,p,m,k
4cab944a 39 double* gam = (double*)malloc(n*k*sizeof(double));
1d3c1faa 40 copyArray(gamInit, gam, n*k);
4cab944a
BA		 41 double* b = (double*)malloc(k*sizeof(double));
42 double* Phi = (double*)malloc(p*m*k*sizeof(double));
43 double* Rho = (double*)malloc(m*m*k*sizeof(double));
44 double* Pi = (double*)malloc(k*sizeof(double));
45 double* gam2 = (double*)malloc(k*sizeof(double));
46 double* pi2 = (double*)malloc(k*sizeof(double));
47 double* Gram2 = (double*)malloc(p*p*k*sizeof(double));
48 double* ps = (double*)malloc(m*k*sizeof(double));
49 double* nY2 = (double*)malloc(m*k*sizeof(double));
50 double* ps1 = (double*)malloc(n*m*k*sizeof(double));
51 double* ps2 = (double*)malloc(p*m*k*sizeof(double));
52 double* nY21 = (double*)malloc(n*m*k*sizeof(double));
53 double* Gam = (double*)malloc(n*k*sizeof(double));
54 double* X2 = (double*)malloc(n*p*k*sizeof(double));
55 double* Y2 = (double*)malloc(n*m*k*sizeof(double));
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BA		 56 gsl_matrix* matrix = gsl_matrix_alloc(m, m);
57 gsl_permutation* permutation = gsl_permutation_alloc(m);
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BA		 58 double* YiRhoR = (double*)malloc(m*sizeof(double));
59 double* XiPhiR = (double*)malloc(m*sizeof(double));
60 double dist = 0.;
61 double dist2 = 0.;
62 int ite = 0;
63 double EPS = 1e-15;
64 double* dotProducts = (double*)malloc(k*sizeof(double));
65
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BA		 66 while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
67 {
68 copyArray(phi, Phi, p*m*k);
69 copyArray(rho, Rho, m*m*k);
70 copyArray(pi, Pi, k);
4cab944a
BA		 71
72 // Calculs associés a Y et X
73 for (int r=0; r<k; r++)
1d3c1faa 74 {
4cab944a 75 for (int mm=0; mm<m; mm++)
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BA		 76 {
77 //Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
4cab944a
BA		 78 for (int u=0; u<n; u++)
79 Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
1d3c1faa 80 }
4cab944a 81 for (int i=0; i<n; i++)
1d3c1faa
BA		 82 {
83 //X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
4cab944a
BA		 84 for (int u=0; u<p; u++)
85 X2[ai(i,u,r,n,m,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
1d3c1faa 86 }
4cab944a 87 for (int mm=0; mm<m; mm++)
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BA		 88 {
89 //ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
4cab944a 90 for (int u=0; u<p; u++)
1d3c1faa 91 {
4cab944a
BA		 92 double dotProduct = 0.;
93 for (int v=0; v<n; v++)
94 dotProduct += X2[ai(v,u,r,n,m,k)] * Y2[ai(v,mm,r,n,m,k)];
95 ps2[ai(u,mm,r,n,m,k)] = dotProduct;
1d3c1faa
BA		 96 }
97 }
4cab944a 98 for (int j=0; j<p; j++)
1d3c1faa 99 {
4cab944a 100 for (int s=0; s<p; s++)
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BA		 101 {
102 //Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
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BA		 103 double dotProduct = 0.;
104 for (int u=0; u<n; u++)
105 dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
106 Gram2[ai(j,s,r,p,p,k)] = dotProduct;
1d3c1faa
BA		 107 }
108 }
109 }
110
111 /////////////
112 // Etape M //
113 /////////////
4cab944a 114
1d3c1faa 115 // Pour pi
4cab944a 116 for (int r=0; r<k; r++)
1d3c1faa
BA		 117 {
118 //b(r) = sum(sum(abs(phi(:,:,r))));
4cab944a
BA		 119 double sumAbsPhi = 0.;
120 for (int u=0; u<p; u++)
121 for (int v=0; v<m; v++)
122 sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
1d3c1faa
BA		 123 b[r] = sumAbsPhi;
124 }
125 //gam2 = sum(gam,1);
4cab944a 126 for (int u=0; u<k; u++)
1d3c1faa 127 {
4cab944a
BA		 128 double sumOnColumn = 0.;
129 for (int v=0; v<n; v++)
130 sumOnColumn += gam[mi(v,u,n,k)];
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BA		 131 gam2[u] = sumOnColumn;
132 }
133 //a=sum(gam*transpose(log(pi)));
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BA		 134 double a = 0.;
135 for (int u=0; u<n; u++)
1d3c1faa 136 {
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BA		 137 double dotProduct = 0.;
138 for (int v=0; v<k; v++)
139 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
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BA		 140 a += dotProduct;
141 }
4cab944a 142
1d3c1faa 143 //tant que les proportions sont negatives
4cab944a 144 int kk = 0;
1d3c1faa 145 int pi2AllPositive = 0;
4cab944a 146 double invN = 1./n;
1d3c1faa
BA		 147 while (!pi2AllPositive)
148 {
149 //pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
4cab944a 150 for (int r=0; r<k; r++)
1d3c1faa
BA		 151 pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
152 pi2AllPositive = 1;
4cab944a 153 for (int r=0; r<k; r++)
1d3c1faa
BA		 154 {
155 if (pi2[r] < 0)
156 {
157 pi2AllPositive = 0;
158 break;
159 }
160 }
161 kk++;
162 }
4cab944a 163
1d3c1faa
BA		 164 //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
165 //(pi.^gamma)*b
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BA		 166 double piPowGammaDotB = 0.;
167 for (int v=0; v<k; v++)
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BA		 168 piPowGammaDotB += pow(pi[v],gamma) * b[v];
169 //(pi2.^gamma)*b
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BA		 170 double pi2PowGammaDotB = 0.;
171 for (int v=0; v<k; v++)
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BA		 172 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
173 //transpose(gam2)*log(pi2)
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BA		 174 double prodGam2logPi2 = 0.;
175 for (int v=0; v<k; v++)
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BA		 176 prodGam2logPi2 += gam2[v] * log(pi2[v]);
177 while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB && kk<1000)
178 {
179 //pi2=pi+0.1^kk*(1/n*gam2-pi);
4cab944a 180 for (int v=0; v<k; v++)
1d3c1faa
BA		 181 pi2[v] = pi[v] + pow(0.1,kk) * (invN*gam2[v] - pi[v]);
182 //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
4cab944a
BA		 183 pi2PowGammaDotB = 0.;
184 for (int v=0; v<k; v++)
1d3c1faa 185 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
4cab944a
BA		 186 prodGam2logPi2 = 0.;
187 for (int v=0; v<k; v++)
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BA		 188 prodGam2logPi2 += gam2[v] * log(pi2[v]);
189 kk++;
190 }
4cab944a 191 double t = pow(0.1,kk);
1d3c1faa 192 //sum(pi+t*(pi2-pi))
4cab944a
BA		 193 double sumPiPlusTbyDiff = 0.;
194 for (int v=0; v<k; v++)
1d3c1faa
BA		 195 sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
196 //pi=(pi+t*(pi2-pi))/sum(pi+t*(pi2-pi));
4cab944a 197 for (int v=0; v<k; v++)
1d3c1faa 198 pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
4cab944a 199
1d3c1faa 200 //Pour phi et rho
4cab944a 201 for (int r=0; r<k; r++)
1d3c1faa 202 {
4cab944a 203 for (int mm=0; mm<m; mm++)
1d3c1faa 204 {
4cab944a 205 for (int i=0; i<n; i++)
1d3c1faa
BA		 206 {
207 //< X2(i,:,r) , phi(:,mm,r) >
4cab944a
BA		 208 double dotProduct = 0.0;
209 for (int u=0; u<p; u++)
210 dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,n,m,k)];
1d3c1faa 211 //ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
4cab944a
BA		 212 ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
213 nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
1d3c1faa
BA		 214 }
215 //ps(mm,r)=sum(ps1(:,mm,r));
4cab944a
BA		 216 double sumPs1 = 0.0;
217 for (int u=0; u<n; u++)
218 sumPs1 += ps1[ai(u,mm,r,n,m,k)];
219 ps[mi(mm,r,m,k)] = sumPs1;
1d3c1faa 220 //nY2(mm,r)=sum(nY21(:,mm,r));
4cab944a
BA		 221 double sumNy21 = 0.0;
222 for (int u=0; u<n; u++)
223 sumNy21 += nY21[ai(u,mm,r,n,m,k)];
224 nY2[mi(mm,r,m,k)] = sumNy21;
1d3c1faa 225 //rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
4cab944a
BA		 226 rho[ai(mm,mm,k,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
227 + 4*nY2[mi(mm,r,m,k)] * (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
1d3c1faa
BA		 228 }
229 }
4cab944a 230 for (int r=0; r<k; r++)
1d3c1faa 231 {
4cab944a 232 for (int j=0; j<p; j++)
1d3c1faa 233 {
4cab944a 234 for (int mm=0; mm<m; mm++)
1d3c1faa
BA		 235 {
236 //sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)))
4cab944a
BA		 237 double dotPhiGram2 = 0.0;
238 for (int u=0; u<j; u++)
239 dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
240 for (int u=j+1; u<p; u++)
241 dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
1d3c1faa
BA		 242 //S(j,r,mm)=-rho(mm,mm,r)*ps2(j,mm,r)+sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))
243 // +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
4cab944a
BA		 244 S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)] + dotPhiGram2;
245 if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow(pi[r],gamma))
246 phi[ai(j,mm,r,p,m,k)] = 0;
247 else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow(pi[r],gamma))
248 phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow(pi[r],gamma) - S[ai(j,mm,r,p,m,k)])
249 / Gram2[ai(j,j,r,p,p,k)];
1d3c1faa 250 else
4cab944a
BA		 251 phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)])
252 / Gram2[ai(j,j,r,p,p,k)];
1d3c1faa
BA		 253 }
254 }
255 }
4cab944a 256
1d3c1faa
BA		 257 /////////////
258 // Etape E //
259 /////////////
4cab944a 260
1d3c1faa 261 int signum;
4cab944a
BA		 262 double sumLogLLF2 = 0.0;
263 for (int i=0; i<n; i++)
1d3c1faa 264 {
4cab944a
BA		 265 double sumLLF1 = 0.0;
266 double sumGamI = 0.0;
267 double minDotProduct = INFINITY;
268
269 for (int r=0; r<k; r++)
1d3c1faa
BA		 270 {
271 //Compute
272 //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
273 // *phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
274 //split in several sub-steps
275
276 //compute Y(i,:)*rho(:,:,r)
4cab944a 277 for (int u=0; u<m; u++)
1d3c1faa
BA		 278 {
279 YiRhoR[u] = 0.0;
4cab944a
BA		 280 for (int v=0; v<m; v++)
281 YiRhoR[u] += Y[imi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
1d3c1faa 282 }
4cab944a 283
1d3c1faa 284 //compute X(i,:)*phi(:,:,r)
4cab944a 285 for (int u=0; u<m; u++)
1d3c1faa
BA		 286 {
287 XiPhiR[u] = 0.0;
4cab944a
BA		 288 for (int v=0; v<p; v++)
289 XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
1d3c1faa 290 }
4cab944a 291
1d3c1faa
BA		 292 // compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
293 dotProducts[r] = 0.0;
4cab944a 294 for (int u=0; u<m; u++)
1d3c1faa
BA		 295 dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
296 if (dotProducts[r] < minDotProduct)
297 minDotProduct = dotProducts[r];
298 }
4cab944a
BA		 299 double shift = 0.5*minDotProduct;
300 for (int r=0; r<k; r++)
1d3c1faa
BA		 301 {
302 //compute det(rho(:,:,r)) [TODO: avoid re-computations]
4cab944a 303 for (int u=0; u<m; u++)
1d3c1faa 304 {
4cab944a
BA		 305 for (int v=0; v<m; v++)
306 matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
1d3c1faa
BA		 307 }
308 gsl_linalg_LU_decomp(matrix, permutation, &signum);
4cab944a
BA		 309 double detRhoR = gsl_linalg_LU_det(matrix, signum);
310
311 Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
312 sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
313 sumGamI += Gam[mi(i,r,n,k)];
1d3c1faa
BA		 314 }
315 sumLogLLF2 += log(sumLLF1);
4cab944a 316 for (int r=0; r<k; r++)
1d3c1faa
BA		 317 {
318 //gam(i,r)=Gam(i,r)/sum(Gam(i,:));
4cab944a
BA		 319 gam[mi(i,r,n,k)] = sumGamI > EPS
320 ? Gam[mi(i,r,n,k)] / sumGamI
1d3c1faa
BA		 321 : 0.0;
322 }
323 }
324
325 //sum(pen(ite,:))
4cab944a
BA		 326 double sumPen = 0.0;
327 for (int r=0; r<k; r++)
1d3c1faa
BA		 328 sumPen += pow(pi[r],gamma) * b[r];
329 //LLF(ite)=-1/n*sum(log(LLF2(ite,:)))+lambda*sum(pen(ite,:));
330 LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
331 if (ite == 0)
332 dist = LLF[ite];
333 else
334 dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
335
336 //Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
4cab944a
BA		 337 double Dist1 = 0.0;
338 for (int u=0; u<p; u++)
1d3c1faa 339 {
4cab944a 340 for (int v=0; v<m; v++)
1d3c1faa 341 {
4cab944a 342 for (int w=0; w<k; w++)
1d3c1faa 343 {
4cab944a
BA		 344 double tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
345 / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
1d3c1faa
BA		 346 if (tmpDist > Dist1)
347 Dist1 = tmpDist;
348 }
349 }
350 }
351 //Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
4cab944a
BA		 352 double Dist2 = 0.0;
353 for (int u=0; u<m; u++)
1d3c1faa 354 {
4cab944a 355 for (int v=0; v<m; v++)
1d3c1faa 356 {
4cab944a 357 for (int w=0; w<k; w++)
1d3c1faa 358 {
4cab944a
BA		 359 double tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
360 / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
1d3c1faa
BA		 361 if (tmpDist > Dist2)
362 Dist2 = tmpDist;
363 }
364 }
365 }
366 //Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
4cab944a
BA		 367 double Dist3 = 0.0;
368 for (int u=0; u<n; u++)
1d3c1faa 369 {
4cab944a 370 for (int v=0; v<k; v++)
1d3c1faa 371 {
4cab944a 372 double tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
1d3c1faa
BA		 373 if (tmpDist > Dist3)
374 Dist3 = tmpDist;
375 }
376 }
377 //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
378 dist2 = Dist1;
379 if (Dist2 > dist2)
380 dist2 = Dist2;
381 if (Dist3 > dist2)
382 dist2 = Dist3;
383
384 ite++;
385 }
386
387 //free memory
388 free(b);
389 free(gam);
390 free(Gam);
391 free(Phi);
392 free(Rho);
393 free(Pi);
394 free(ps);
395 free(nY2);
396 free(ps1);
397 free(nY21);
398 free(Gram2);
399 free(ps2);
400 gsl_matrix_free(matrix);
401 gsl_permutation_free(permutation);
402 free(XiPhiR);
403 free(YiRhoR);
404 free(gam2);
405 free(pi2);
406 free(X2);
407 free(Y2);
408 free(dotProducts);
409}
Variable selection with mixtures of models