src/sources/EMGLLF.c

   1 #include "utils.h"
   2 #include <stdlib.h>
   3 #include <gsl/gsl_linalg.h>
   4
   5 // TODO: don't recompute indexes every time......
   6 void EMGLLF_core(
   7     // IN parameters
   8     const Real* phiInit, // parametre initial de moyenne renormalisé
   9     const Real* rhoInit, // parametre initial de variance renormalisé
  10     const Real* piInit,  // parametre initial des proportions
  11     const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
  12     int mini, // nombre minimal d'itérations dans l'algorithme EM
  13     int maxi, // nombre maximal d'itérations dans l'algorithme EM
  14     Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
  15     Real lambda, // valeur du paramètre de régularisation du Lasso
  16     const Real* X, // régresseurs
  17     const Real* Y, // réponse
  18     Real tau, // seuil pour accepter la convergence
  19     // OUT parameters (all pointers, to be modified)
  20     Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
  21     Real* rho, // parametre de variance renormalisé, calculé par l'EM
  22     Real* pi, // parametre des proportions renormalisé, calculé par l'EM
  23     Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
  24     Real* S,
  25     // additional size parameters
  26     int n, // nombre d'echantillons
  27     int p, // nombre de covariables
  28     int m, // taille de Y (multivarié)
  29     int k) // nombre de composantes dans le mélange
  30 {
  31     //Initialize outputs
  32     copyArray(phiInit, phi, p*m*k);
  33     copyArray(rhoInit, rho, m*m*k);
  34     copyArray(piInit, pi, k);
  35     zeroArray(LLF, maxi);
  36     //S is already allocated, and doesn't need to be 'zeroed'
  37
  38     //Other local variables
  39     //NOTE: variables order is always [maxi],n,p,m,k
  40     Real* gam = (Real*)malloc(n*k*sizeof(Real));
  41     copyArray(gamInit, gam, n*k);
  42     Real* b = (Real*)malloc(k*sizeof(Real));
  43     Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
  44     Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
  45     Real* Pi = (Real*)malloc(k*sizeof(Real));
  46     Real* gam2 = (Real*)malloc(k*sizeof(Real));
  47     Real* pi2 = (Real*)malloc(k*sizeof(Real));
  48     Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
  49     Real* ps = (Real*)malloc(m*k*sizeof(Real));
  50     Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
  51     Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
  52     Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
  53     Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
  54     Real* Gam = (Real*)malloc(n*k*sizeof(Real));
  55     Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
  56     Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
  57     gsl_matrix* matrix = gsl_matrix_alloc(m, m);
  58     gsl_permutation* permutation = gsl_permutation_alloc(m);
  59     Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
  60     Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
  61     Real dist = 0.;
  62     Real dist2 = 0.;
  63     int ite = 0;
  64     Real EPS = 1e-15;
  65     Real* dotProducts = (Real*)malloc(k*sizeof(Real));
  66
  67     while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
  68     {
  69         copyArray(phi, Phi, p*m*k);
  70         copyArray(rho, Rho, m*m*k);
  71         copyArray(pi, Pi, k);
  72
  73         // Calculs associés a Y et X
  74         for (int r=0; r<k; r++)
  75         {
  76             for (int mm=0; mm<m; mm++)
  77             {
  78                 //Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
  79                 for (int u=0; u<n; u++)
  80                     Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
  81             }
  82             for (int i=0; i<n; i++)
  83             {
  84                 //X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
  85                 for (int u=0; u<p; u++)
  86                     X2[ai(i,u,r,n,m,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
  87             }
  88             for (int mm=0; mm<m; mm++)
  89             {
  90                 //ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
  91                 for (int u=0; u<p; u++)
  92                 {
  93                     Real dotProduct = 0.;
  94                     for (int v=0; v<n; v++)
  95                         dotProduct += X2[ai(v,u,r,n,m,k)] * Y2[ai(v,mm,r,n,m,k)];
  96                     ps2[ai(u,mm,r,n,m,k)] = dotProduct;
  97                 }
  98             }
  99             for (int j=0; j<p; j++)
 100             {
 101                 for (int s=0; s<p; s++)
 102                 {
 103                     //Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
 104                     Real dotProduct = 0.;
 105                     for (int u=0; u<n; u++)
 106                         dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
 107                     Gram2[ai(j,s,r,p,p,k)] = dotProduct;
 108                 }
 109             }
 110         }
 111
 112         /////////////
 113         // Etape M //
 114         /////////////
 115
 116         // Pour pi
 117         for (int r=0; r<k; r++)
 118         {
 119             //b(r) = sum(sum(abs(phi(:,:,r))));
 120             Real sumAbsPhi = 0.;
 121             for (int u=0; u<p; u++)
 122                 for (int v=0; v<m; v++)
 123                     sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
 124             b[r] = sumAbsPhi;
 125         }
 126         //gam2 = sum(gam,1);
 127         for (int u=0; u<k; u++)
 128         {
 129             Real sumOnColumn = 0.;
 130             for (int v=0; v<n; v++)
 131                 sumOnColumn += gam[mi(v,u,n,k)];
 132             gam2[u] = sumOnColumn;
 133         }
 134         //a=sum(gam*transpose(log(pi)));
 135         Real a = 0.;
 136         for (int u=0; u<n; u++)
 137         {
 138             Real dotProduct = 0.;
 139             for (int v=0; v<k; v++)
 140                 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
 141             a += dotProduct;
 142         }
 143
 144         //tant que les proportions sont negatives
 145         int kk = 0;
 146         int pi2AllPositive = 0;
 147         Real invN = 1./n;
 148         while (!pi2AllPositive)
 149         {
 150             //pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
 151             for (int r=0; r<k; r++)
 152                 pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
 153             pi2AllPositive = 1;
 154             for (int r=0; r<k; r++)
 155             {
 156                 if (pi2[r] < 0)
 157                 {
 158                     pi2AllPositive = 0;
 159                     break;
 160                 }
 161             }
 162             kk++;
 163         }
 164
 165         //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
 166         //(pi.^gamma)*b
 167         Real piPowGammaDotB = 0.;
 168         for (int v=0; v<k; v++)
 169             piPowGammaDotB += pow(pi[v],gamma) * b[v];
 170         //(pi2.^gamma)*b
 171         Real pi2PowGammaDotB = 0.;
 172         for (int v=0; v<k; v++)
 173             pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 174         //transpose(gam2)*log(pi2)
 175         Real prodGam2logPi2 = 0.;
 176         for (int v=0; v<k; v++)
 177             prodGam2logPi2 += gam2[v] * log(pi2[v]);
 178         while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
 179             && kk<1000)
 180         {
 181             //pi2=pi+0.1^kk*(1/n*gam2-pi);
 182             for (int v=0; v<k; v++)
 183                 pi2[v] = pi[v] + pow(0.1,kk) * (invN*gam2[v] - pi[v]);
 184             //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
 185             pi2PowGammaDotB = 0.;
 186             for (int v=0; v<k; v++)
 187                 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 188             prodGam2logPi2 = 0.;
 189             for (int v=0; v<k; v++)
 190                 prodGam2logPi2 += gam2[v] * log(pi2[v]);
 191             kk++;
 192         }
 193         Real t = pow(0.1,kk);
 194         //sum(pi+t*(pi2-pi))
 195         Real sumPiPlusTbyDiff = 0.;
 196         for (int v=0; v<k; v++)
 197             sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
 198         //pi=(pi+t*(pi2-pi))/sum(pi+t*(pi2-pi));
 199         for (int v=0; v<k; v++)
 200             pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
 201
 202         //Pour phi et rho
 203         for (int r=0; r<k; r++)
 204         {
 205             for (int mm=0; mm<m; mm++)
 206             {
 207                 for (int i=0; i<n; i++)
 208                 {
 209                     //< X2(i,:,r) , phi(:,mm,r) >
 210                     Real dotProduct = 0.0;
 211                     for (int u=0; u<p; u++)
 212                         dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
 213                     //ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
 214                     ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
 215                     nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
 216                 }
 217                 //ps(mm,r)=sum(ps1(:,mm,r));
 218                 Real sumPs1 = 0.0;
 219                 for (int u=0; u<n; u++)
 220                     sumPs1 += ps1[ai(u,mm,r,n,m,k)];
 221                 ps[mi(mm,r,m,k)] = sumPs1;
 222                 //nY2(mm,r)=sum(nY21(:,mm,r));
 223
 224
 225                 Real sumNy21 = sqrt(sumPs1); //0.0; ////////////TODO: 0.0 is correct; valgrind says that sumPs1 is uninitialized............
 226
 227
 228                 for (int u=0; u<n; u++)
 229                     sumNy21 += nY21[ai(u,mm,r,n,m,k)];
 230                 nY2[mi(mm,r,m,k)] = sumNy21;
 231                 //rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
 232                 rho[ai(mm,mm,r,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
 233                     + 4*nY2[mi(mm,r,m,k)] * (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
 234             }
 235         }
 236         for (int r=0; r<k; r++)
 237         {
 238             for (int j=0; j<p; j++)
 239             {
 240                 for (int mm=0; mm<m; mm++)
 241                 {
 242                     //sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r)
 243                     // .*transpose(Gram2(j,j+1:p,r)))
 244                     Real dotPhiGram2 = 0.0;
 245                     for (int u=0; u<j; u++)
 246                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 247                     for (int u=j+1; u<p; u++)
 248                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 249                     //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)))
 250                     //      +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
 251                     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;
 252                     if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow(pi[r],gamma))
 253                         phi[ai(j,mm,r,p,m,k)] = 0;
 254                     else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow(pi[r],gamma))
 255                         phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow(pi[r],gamma) - S[ai(j,mm,r,p,m,k)])
 256                             / Gram2[ai(j,j,r,p,p,k)];
 257                     else
 258                         phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)])
 259                             / Gram2[ai(j,j,r,p,p,k)];
 260                 }
 261             }
 262         }
 263
 264         /////////////
 265         // Etape E //
 266         /////////////
 267
 268         int signum;
 269         Real sumLogLLF2 = 0.0;
 270         for (int i=0; i<n; i++)
 271         {
 272             Real sumLLF1 = 0.0;
 273             Real sumGamI = 0.0;
 274             Real minDotProduct = INFINITY;
 275
 276             for (int r=0; r<k; r++)
 277             {
 278                 //Compute
 279                 //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
 280                 //      *phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
 281                 //split in several sub-steps
 282
 283                 //compute Y(i,:)*rho(:,:,r)
 284                 for (int u=0; u<m; u++)
 285                 {
 286                     YiRhoR[u] = 0.0;
 287                     for (int v=0; v<m; v++)
 288                         YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 289                 }
 290
 291                 //compute X(i,:)*phi(:,:,r)
 292                 for (int u=0; u<m; u++)
 293                 {
 294                     XiPhiR[u] = 0.0;
 295                     for (int v=0; v<p; v++)
 296                         XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 297                 }
 298
 299                 //compute dotProduct
 300                 // < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
 301                 dotProducts[r] = 0.0;
 302                 for (int u=0; u<m; u++)
 303                     dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
 304                 if (dotProducts[r] < minDotProduct)
 305                     minDotProduct = dotProducts[r];
 306             }
 307             Real shift = 0.5*minDotProduct;
 308             for (int r=0; r<k; r++)
 309             {
 310                 //compute det(rho(:,:,r)) [TODO: avoid re-computations]
 311                 for (int u=0; u<m; u++)
 312                 {
 313                     for (int v=0; v<m; v++)
 314                         matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 315                 }
 316                 gsl_linalg_LU_decomp(matrix, permutation, &signum);
 317                 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
 318
 319                 Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
 320                 sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
 321                 sumGamI += Gam[mi(i,r,n,k)];
 322             }
 323             sumLogLLF2 += log(sumLLF1);
 324             for (int r=0; r<k; r++)
 325             {
 326                 //gam(i,r)=Gam(i,r)/sum(Gam(i,:));
 327                 gam[mi(i,r,n,k)] = sumGamI > EPS
 328                     ? Gam[mi(i,r,n,k)] / sumGamI
 329                     : 0.0;
 330             }
 331         }
 332
 333         //sum(pen(ite,:))
 334         Real sumPen = 0.0;
 335         for (int r=0; r<k; r++)
 336             sumPen += pow(pi[r],gamma) * b[r];
 337         //LLF(ite)=-1/n*sum(log(LLF2(ite,:)))+lambda*sum(pen(ite,:));
 338         LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
 339         if (ite == 0)
 340             dist = LLF[ite];
 341         else
 342             dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
 343
 344         //Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
 345         Real Dist1 = 0.0;
 346         for (int u=0; u<p; u++)
 347         {
 348             for (int v=0; v<m; v++)
 349             {
 350                 for (int w=0; w<k; w++)
 351                 {
 352                     Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
 353                         / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
 354                     if (tmpDist > Dist1)
 355                         Dist1 = tmpDist;
 356                 }
 357             }
 358         }
 359         //Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
 360         Real Dist2 = 0.0;
 361         for (int u=0; u<m; u++)
 362         {
 363             for (int v=0; v<m; v++)
 364             {
 365                 for (int w=0; w<k; w++)
 366                 {
 367                     Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
 368                         / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
 369                     if (tmpDist > Dist2)
 370                         Dist2 = tmpDist;
 371                 }
 372             }
 373         }
 374         //Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
 375         Real Dist3 = 0.0;
 376         for (int u=0; u<n; u++)
 377         {
 378             for (int v=0; v<k; v++)
 379             {
 380                 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
 381                 if (tmpDist > Dist3)
 382                     Dist3 = tmpDist;
 383             }
 384         }
 385         //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
 386         dist2 = Dist1;
 387         if (Dist2 > dist2)
 388             dist2 = Dist2;
 389         if (Dist3 > dist2)
 390             dist2 = Dist3;
 391
 392         ite++;
 393     }
 394
 395     //free memory
 396     free(b);
 397     free(gam);
 398     free(Gam);
 399     free(Phi);
 400     free(Rho);
 401     free(Pi);
 402     free(ps);
 403     free(nY2);
 404     free(ps1);
 405     free(nY21);
 406     free(Gram2);
 407     free(ps2);
 408     gsl_matrix_free(matrix);
 409     gsl_permutation_free(permutation);
 410     free(XiPhiR);
 411     free(YiRhoR);
 412     free(gam2);
 413     free(pi2);
 414     free(X2);
 415     free(Y2);
 416     free(dotProducts);
 417 }