void maximization(llna_model* model, llna_ss* ss)
{
int i, j;
double sum;
// mean maximization
for (i = 0; i < model->k-1; i++)
vset(model->mu, i, vget(ss->mu_ss, i) / ss->ndata);
// covariance maximization
for (i = 0; i < model->k-1; i++)
{
for (j = 0; j < model->k-1; j++)
{
mset(model->cov, i, j,
(1.0 / ss->ndata) *
(mget(ss->cov_ss, i, j) +
ss->ndata * vget(model->mu, i) * vget(model->mu, j) -
vget(ss->mu_ss, i) * vget(model->mu, j) -
vget(ss->mu_ss, j) * vget(model->mu, i)));
}
}
if (PARAMS.cov_estimate == SHRINK)
{
cov_shrinkage(model->cov, ss->ndata, model->cov);
}
matrix_inverse(model->cov, model->inv_cov);
model->log_det_inv_cov = log_det(model->inv_cov);
// topic maximization
for (i = 0; i < model->k; i++)
{
sum = 0;
for (j = 0; j < model->log_beta->size2; j++)
sum += mget(ss->beta_ss, i, j);
if (sum == 0) sum = safe_log(sum) * model->log_beta->size2;
else sum = safe_log(sum);
for (j = 0; j < model->log_beta->size2; j++)
mset(model->log_beta, i, j, safe_log(mget(ss->beta_ss, i, j)) - sum);
}
}
rowvec laNRb(const rowvec &data, const mat &iS, const double &detS,
const rowvec &mu0, const rowvec &mu1, const rowvec &mu2,
const rowvec &lambda0, const rowvec &lambda1, const rowvec &lambda2,
const rowvec &beta0, const rowvec &beta1, const rowvec &beta2,
const rowvec &gamma, const rowvec &gamma2,
const double &Dtol, const unsigned &niter, const double &lambda) {
rowvec eta = zeros(1,3);
for (unsigned i=0; i<niter; i++) {
hObj K = hb(eta,data,iS,
mu0,mu1,mu2,lambda0,lambda1,lambda2,beta0,beta1,beta2,gamma,gamma2);
double Sabs = as_scalar(trans(K.grad)*K.grad);
if (Sabs<Dtol) break;
// mat Delta = trans(K.grad)*inv(K.hess + 0.1*eye(K.hess.n_cols,K.hess.n_cols));
mat Delta = trans(K.grad)*inv(K.hess);
eta = eta-lambda*Delta;
// hObj K = h(eta1,data,iS,
// mu1,mu2,lambda1,lambda2,beta,gamma);
}
hObj K = hb(eta,data,iS,
mu0,mu1,mu2,lambda0,lambda1,lambda2,beta0,beta1,beta2,gamma,gamma2);
// cerr << "K.grad=" << K.grad << endl;
double logHdet;
double sign;
log_det(logHdet,sign,K.hess); // log(det(-K.hess))
if (std::isnan(logHdet)) logHdet = -1000;
double logI = K.hSh - 0.5*(logHdet+log(detS));
// double logI = K.hSh - 0.5*log(detS);
// cerr << "logI" << logI << endl;
// cerr << "hess" << -K.hess << endl;
// cerr << "hSh" << -K.hSh << endl;
rowvec res(4);
res(0) = logI; for (unsigned i=0; i<3; i++) res(i+1) = eta(i);
return(res);
}
double log_like_plus_log_prior(vec y, mat X, vec param, mat I, vec priors) {
double ls2 = param[0];
double w = param[1];
double ltau = param[2];
vec d_vec = param.tail( param.size()-3 );
vec d2 = d_vec % d_vec;
mat D_mat = xDx(X,d2); // ORIGINAL and best so far
//mat D_mat = xDx(X,d2/sum(d2));
double a_s2 = priors[0];//2;
double b_s2 = priors[1];//5;
double a_phi = priors[2];//0;
double b_phi = priors[3];//5;
double a_tau = priors[4];//2;
double b_tau = priors[5];//5;
double a_d = priors[6]; //1;
double b_d = priors[7]; //1;
double s2 = exp(ls2);
double phi = (b_phi*exp(w) + a_phi) / (exp(w)+1); // inverse logit
double tau = exp(ltau);
mat K = tau * exp(-phi*D_mat);
double ldet_K,sign;
mat s2I_plus_K = s2*I + K;
log_det(ldet_K, sign, s2I_plus_K);
double sum_log_dj_prior = sum( (-b_d-1) * log(1+abs(d_vec) / (a_d * b_d)) );
double log_prior = ( w-2*log(exp(w)+1) ) - a_s2*ls2 - b_s2/s2 - a_tau*ltau - b_tau/tau + sum_log_dj_prior;
double log_like = (-.5 * ldet_K - .5 * y.t() * s2I_plus_K.i() * y)[0];
return log_like + log_prior;
}
//Calculation of BICreg
List Vect::bicReggen(vector<int> vectH, vector<int> vectY, int numr)
{
double reg = 0.0, sign, val;
// Ici, H est la matrice réponse.
mat H=Vect::const_matrix(vectH);
int n = H.n_rows,v = H.n_cols;
//construction of the matrix X
int a;
if (vectY.empty())
a=0;
else
a=vectY.size();
mat X(n,a+1);
if (vectY.empty())
X.col(0) = ones<colvec>(n);
else
{
mat Y = Vect::const_matrix(vectY);
Y.insert_cols(0, ones<colvec>(n));
X = Y;
}
//Parameter estimation
mat XtX = X.t() * X;
mat B = inv_sympd(XtX) * X.t() *H;
//mat B = pinv(XtX) * X.t() *H;
double lambda;
mat A=X*B;
if (numr==3) //(r=[LC])
{
mat Omega = (1.0/n)*(H.t()*(H-A));
Omega = 2*M_PI*Omega;
log_det(val, sign, Omega);
double det = log(sign*exp(val));
lambda = ((a+1)*v) + (0.5*v*(v+1));
reg = (-n*det)-(n*v)-(lambda*log(n));
}
if (numr==2) //(r=[LB])
{
mat H_A = (1.0/n)*(H - A)%(H - A);
rowvec sigma2 = sum(H_A, 0);
sigma2 = log(sigma2);
lambda=(v*(a+1)) +v;
reg=-(n*v*log(2*M_PI)) - (n* sum(sigma2)) -(n*v) - (lambda*log(n));
}
if (numr==1) //(r=[LI])
{
mat Aux=H-A;
double sigma=(1.0/(n*v))* accu(Aux % Aux);
lambda=(v*(a+1)) + 1;
reg=-(n*v*log(2*M_PI*sigma)) -(n*v) - (lambda*log(n));
}
return List::create(Named("bicvalue") = reg,
Named("B") = B);
}//end Vect::bicReggen
