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 double* phiInit, // parametre initial de moyenne renormalisé
   9     const double* rhoInit, // parametre initial de variance renormalisé
  10     const double* piInit,    // parametre initial des proportions
  11     const double* 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     double gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
  15     double lambda, // valeur du paramètre de régularisation du Lasso
  16     const double* X, // régresseurs
  17     const double* Y, // réponse
  18     double tau, // seuil pour accepter la convergence
  19     // OUT parameters (all pointers, to be modified)
  20     double* phi, // parametre de moyenne renormalisé, calculé par l'EM
  21     double* rho, // parametre de variance renormalisé, calculé par l'EM
  22     double* pi, // parametre des proportions renormalisé, calculé par l'EM
  23     double* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
  24     double* 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     double* gam = (double*)malloc(n*k*sizeof(double));
  41     copyArray(gamInit, gam, n*k);
  42     double* b = (double*)malloc(k*sizeof(double));
  43     double* Phi = (double*)malloc(p*m*k*sizeof(double));
  44     double* Rho = (double*)malloc(m*m*k*sizeof(double));
  45     double* Pi = (double*)malloc(k*sizeof(double));
  46     double* gam2 = (double*)malloc(k*sizeof(double));
  47     double* pi2 = (double*)malloc(k*sizeof(double));
  48     double* Gram2 = (double*)malloc(p*p*k*sizeof(double));
  49     double* ps = (double*)malloc(m*k*sizeof(double));
  50     double* nY2 = (double*)malloc(m*k*sizeof(double));
  51     double* ps1 = (double*)malloc(n*m*k*sizeof(double));
  52     double* ps2 = (double*)malloc(p*m*k*sizeof(double));
  53     double* nY21 = (double*)malloc(n*m*k*sizeof(double));
  54     double* Gam = (double*)malloc(n*k*sizeof(double));
  55     double* X2 = (double*)malloc(n*p*k*sizeof(double));
  56     double* Y2 = (double*)malloc(n*m*k*sizeof(double));
  57     gsl_matrix* matrix = gsl_matrix_alloc(m, m);
  58     gsl_permutation* permutation = gsl_permutation_alloc(m);
  59     double* YiRhoR = (double*)malloc(m*sizeof(double));
  60     double* XiPhiR = (double*)malloc(m*sizeof(double));
  61     double dist = 0.;
  62     double dist2 = 0.;
  63     int ite = 0;
  64     double EPS = 1e-15;
  65     double* dotProducts = (double*)malloc(k*sizeof(double));
  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                     double 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                     double 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             double 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             double 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         double a = 0.;
 136         for (int u=0; u<n; u++)
 137         {
 138             double 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         double 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         double piPowGammaDotB = 0.;
 168         for (int v=0; v<k; v++)
 169             piPowGammaDotB += pow(pi[v],gamma) * b[v];
 170         //(pi2.^gamma)*b
 171         double pi2PowGammaDotB = 0.;
 172         for (int v=0; v<k; v++)
 173             pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 174         //transpose(gam2)*log(pi2)
 175         double 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         double t = pow(0.1,kk);
 194         //sum(pi+t*(pi2-pi))
 195         double 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                     double 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,n,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                 double 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                 double sumNy21 = 0.0;
 224                 for (int u=0; u<n; u++)
 225                     sumNy21 += nY21[ai(u,mm,r,n,m,k)];
 226                 nY2[mi(mm,r,m,k)] = sumNy21;
 227                 //rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
 228                 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)]
 229                     + 4*nY2[mi(mm,r,m,k)] * (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
 230             }
 231         }
 232         for (int r=0; r<k; r++)
 233         {
 234             for (int j=0; j<p; j++)
 235             {
 236                 for (int mm=0; mm<m; mm++)
 237                 {
 238                     //sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r)
 239                     // .*transpose(Gram2(j,j+1:p,r)))
 240                     double dotPhiGram2 = 0.0;
 241                     for (int u=0; u<j; u++)
 242                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 243                     for (int u=j+1; u<p; u++)
 244                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 245                     //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)))
 246                     //      +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
 247                     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;
 248                     if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow(pi[r],gamma))
 249                         phi[ai(j,mm,r,p,m,k)] = 0;
 250                     else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow(pi[r],gamma))
 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)];
 253                     else
 254                         phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)])
 255                             / Gram2[ai(j,j,r,p,p,k)];
 256                 }
 257             }
 258         }
 259
 260         /////////////
 261         // Etape E //
 262         /////////////
 263
 264         int signum;
 265         double sumLogLLF2 = 0.0;
 266         for (int i=0; i<n; i++)
 267         {
 268             double sumLLF1 = 0.0;
 269             double sumGamI = 0.0;
 270             double minDotProduct = INFINITY;
 271
 272             for (int r=0; r<k; r++)
 273             {
 274                 //Compute
 275                 //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
 276                 //      *phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
 277                 //split in several sub-steps
 278
 279                 //compute Y(i,:)*rho(:,:,r)
 280                 for (int u=0; u<m; u++)
 281                 {
 282                     YiRhoR[u] = 0.0;
 283                     for (int v=0; v<m; v++)
 284                         YiRhoR[u] += Y[imi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 285                 }
 286
 287                 //compute X(i,:)*phi(:,:,r)
 288                 for (int u=0; u<m; u++)
 289                 {
 290                     XiPhiR[u] = 0.0;
 291                     for (int v=0; v<p; v++)
 292                         XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 293                 }
 294
 295                 //compute dotProduct
 296                 // < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
 297                 dotProducts[r] = 0.0;
 298                 for (int u=0; u<m; u++)
 299                     dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
 300                 if (dotProducts[r] < minDotProduct)
 301                     minDotProduct = dotProducts[r];
 302             }
 303             double shift = 0.5*minDotProduct;
 304             for (int r=0; r<k; r++)
 305             {
 306                 //compute det(rho(:,:,r)) [TODO: avoid re-computations]
 307                 for (int u=0; u<m; u++)
 308                 {
 309                     for (int v=0; v<m; v++)
 310                         matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 311                 }
 312                 gsl_linalg_LU_decomp(matrix, permutation, &signum);
 313                 double detRhoR = gsl_linalg_LU_det(matrix, signum);
 314
 315                 Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
 316                 sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
 317                 sumGamI += Gam[mi(i,r,n,k)];
 318             }
 319             sumLogLLF2 += log(sumLLF1);
 320             for (int r=0; r<k; r++)
 321             {
 322                 //gam(i,r)=Gam(i,r)/sum(Gam(i,:));
 323                 gam[mi(i,r,n,k)] = sumGamI > EPS
 324                     ? Gam[mi(i,r,n,k)] / sumGamI
 325                     : 0.0;
 326             }
 327         }
 328
 329         //sum(pen(ite,:))
 330         double sumPen = 0.0;
 331         for (int r=0; r<k; r++)
 332             sumPen += pow(pi[r],gamma) * b[r];
 333         //LLF(ite)=-1/n*sum(log(LLF2(ite,:)))+lambda*sum(pen(ite,:));
 334         LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
 335         if (ite == 0)
 336             dist = LLF[ite];
 337         else
 338             dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
 339
 340         //Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
 341         double Dist1 = 0.0;
 342         for (int u=0; u<p; u++)
 343         {
 344             for (int v=0; v<m; v++)
 345             {
 346                 for (int w=0; w<k; w++)
 347                 {
 348                     double tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
 349                         / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
 350                     if (tmpDist > Dist1)
 351                         Dist1 = tmpDist;
 352                 }
 353             }
 354         }
 355         //Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
 356         double Dist2 = 0.0;
 357         for (int u=0; u<m; u++)
 358         {
 359             for (int v=0; v<m; v++)
 360             {
 361                 for (int w=0; w<k; w++)
 362                 {
 363                     double tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
 364                         / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
 365                     if (tmpDist > Dist2)
 366                         Dist2 = tmpDist;
 367                 }
 368             }
 369         }
 370         //Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
 371         double Dist3 = 0.0;
 372         for (int u=0; u<n; u++)
 373         {
 374             for (int v=0; v<k; v++)
 375             {
 376                 double tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
 377                 if (tmpDist > Dist3)
 378                     Dist3 = tmpDist;
 379             }
 380         }
 381         //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
 382         dist2 = Dist1;
 383         if (Dist2 > dist2)
 384             dist2 = Dist2;
 385         if (Dist3 > dist2)
 386             dist2 = Dist3;
 387
 388         ite++;
 389     }
 390
 391     //free memory
 392     free(b);
 393     free(gam);
 394     free(Gam);
 395     free(Phi);
 396     free(Rho);
 397     free(Pi);
 398     free(ps);
 399     free(nY2);
 400     free(ps1);
 401     free(nY21);
 402     free(Gram2);
 403     free(ps2);
 404     gsl_matrix_free(matrix);
 405     gsl_permutation_free(permutation);
 406     free(XiPhiR);
 407     free(YiRhoR);
 408     free(gam2);
 409     free(pi2);
 410     free(X2);
 411     free(Y2);
 412     free(dotProducts);
 413 }