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