List EM(const arma::mat& transition_, const arma::cube& emission_, const arma::vec& init_,
const arma::ucube& obs, const arma::uvec& nSymbols, int itermax, double tol,
int trace, unsigned int threads) {
// Make sure we don't alter the original vec/mat/cube
// needed for cube, in future maybe in other cases as well
arma::cube emission(emission_);
arma::mat transition(transition_);
arma::vec init(init_);
// EM-algorithm begins
double change = tol + 1.0;
int iter = -1; //for backward compatibility
double sumlogLik_new = 0;
double sumlogLik = -1e150; //sum(ll);
while ((change > tol) & (iter < itermax)) {
iter++;
arma::mat ksii(emission.n_rows, emission.n_rows, arma::fill::zeros);
arma::cube gamma(emission.n_rows, emission.n_cols, emission.n_slices, arma::fill::zeros);
arma::vec delta(emission.n_rows, arma::fill::zeros);
sumlogLik_new = 0;
double max_sf = 1;
unsigned int error_code = 0;
#pragma omp parallel for if(obs.n_slices>=threads) schedule(static) reduction(+:sumlogLik_new) num_threads(threads) \
default(none) shared(init, transition, obs, emission, delta, ksii, gamma, nSymbols, error_code, max_sf)
for (unsigned int k = 0; k < obs.n_slices; k++) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n,k
arma::vec scales(obs.n_cols);
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, init, obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n,k
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
sumlogLik_new -= arma::sum(log(scales));
arma::mat ksii_k(emission.n_rows, emission.n_rows, arma::fill::zeros);
arma::cube gamma_k(emission.n_rows, emission.n_cols, emission.n_slices, arma::fill::zeros);
arma::vec delta_k(emission.n_rows);
delta_k = alpha.col(0) % beta.col(0);
if (obs.n_cols > 1) {
for (unsigned int j = 0; j < emission.n_rows; j++) {
for (unsigned int i = 0; i < emission.n_rows; i++) {
if (transition(i, j) > 0.0) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(i, t) * transition(i, j) * beta(j, t + 1)
* scales(t + 1);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, t + 1, k), r);
}
ksii_k(i, j) += tmp;
}
}
}
}
}
for (unsigned int r = 0; r < emission.n_slices; r++) {
for (unsigned int l = 0; l < nSymbols(r); l++) {
for (unsigned int i = 0; i < emission.n_rows; i++) {
if (emission(i, l, r) > 0.0) {
for (unsigned int t = 0; t < obs.n_cols; t++) {
if (l == (obs(r, t, k))) {
gamma_k(i, l, r) += alpha(i, t) * beta(i, t);
}
}
}
}
}
}
#pragma omp critical
{
if(!scales.is_finite()) {
error_code = 1;
}
if(!beta.is_finite()) {
error_code = 2;
}
max_sf = std::min(max_sf, scales.max());
delta += delta_k;
ksii += ksii_k;
gamma += gamma_k;
}
}
if(error_code == 1) {
return List::create(Named("error") = 1);
}
if(error_code == 2) {
return List::create(Named("error") = 2);
}
if (max_sf > 1e150) {
Rcpp::warning("Largest scaling factor was %e, results can be numerically unstable.", max_sf);
}
change = (sumlogLik_new - sumlogLik) / (std::abs(sumlogLik) + 0.1);
sumlogLik = sumlogLik_new;
if (trace > 0) {
if(iter == 1) {
Rcout << "Log-likelihood of initial model: " << sumlogLik << std::endl;
} else {
if (trace > 1) {
Rcout << "iter: " << iter;
Rcout << " logLik: " << sumlogLik;
Rcout << " relative change: " << change << std::endl;
}
}
}
if (change > tol) {
if (obs.n_cols > 1) {
ksii.each_col() /= sum(ksii, 1);
transition = ksii;
}
for (unsigned int r = 0; r < emission.n_slices; r++) {
gamma.slice(r).cols(0, nSymbols(r) - 1).each_col() /= sum(
gamma.slice(r).cols(0, nSymbols(r) - 1), 1);
emission.slice(r).cols(0, nSymbols(r) - 1) = gamma.slice(r).cols(0, nSymbols(r) - 1);
}
delta /= arma::as_scalar(arma::accu(delta));
init = delta;
}
// internalForward(transition, emission, init, obs, alpha, scales, threads);
// if(!scales.is_finite()) {
// return List::create(Named("error") = 1);
// }
// internalBackward(transition, emission, obs, beta, scales, threads);
// if(!beta.is_finite()) {
// return List::create(Named("error") = 2);
// }
// double min_sf = scales.min();
// if (min_sf < 1e-150) {
// Rcpp::warning("Smallest scaling factor was %e, results can be numerically unstable.", min_sf);
// }
//
// ll = sum(log(scales));
//double tmp = sum(ll);
}
if (trace > 0) {
if (iter == itermax) {
Rcpp::Rcout << "EM algorithm stopped after reaching the maximum number of " << iter
<< " iterations." << std::endl;
} else {
Rcpp::Rcout << "EM algorithm stopped after reaching the relative change of " << change;
Rcpp::Rcout << " after " << iter << " iterations." << std::endl;
}
Rcpp::Rcout << "Final log-likelihood: " << sumlogLik << std::endl;
}
return List::create(Named("initialProbs") = wrap(init),
Named("transitionMatrix") = wrap(transition), Named("emissionArray") = wrap(emission),
Named("logLik") = sumlogLik, Named("iterations") = iter, Named("change") = change, Named("error") = 0);
}
List objectivex(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, const arma::ucube& obs, const arma::umat& ANZ,
const arma::ucube& BNZ, const arma::uvec& INZ, const arma::uvec& nSymbols,
const arma::mat& coef, const arma::mat& X, arma::uvec& numberOfStates,
unsigned int threads) {
unsigned int q = coef.n_rows;
arma::vec grad(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
arma::fill::zeros);
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
grad.fill(-arma::datum::inf);
return List::create(Named("objective") = arma::datum::inf, Named("gradient") = wrap(grad));
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
arma::uvec cumsumstate = arma::cumsum(numberOfStates);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(none) shared(q, grad, nSymbols, ANZ, BNZ, INZ, \
numberOfStates, cumsumstate, obs, init, initk, X, weights, transition, emission, error)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, initk.col(k), obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
if (arma::accu(ANZ) > 0) {
for (unsigned int jj = 0; jj < numberOfStates.n_elem; jj++) {
arma::vec gradArow(numberOfStates(jj));
arma::mat gradA(numberOfStates(jj), numberOfStates(jj));
int ind_jj = cumsumstate(jj) - numberOfStates(jj);
for (unsigned int i = 0; i < numberOfStates(jj); i++) {
arma::uvec ind = arma::find(ANZ.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1);
gradA.each_col() %= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1).t();
for (unsigned int j = 0; j < numberOfStates(jj); j++) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(ind_jj + i, t);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_jj + j, obs(r, t + 1, k), r);
}
gradArow(j) += tmp * beta(ind_jj + j, t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(BNZ) > 0) {
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (unsigned int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = initk(i, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += tmp * beta(i, 0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = beta(i, t + 1);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp;
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(INZ) > 0) {
for (unsigned int i = 0; i < numberOfStates.n_elem; i++) {
int ind_i = cumsumstate(i) - numberOfStates(i);
arma::uvec ind = arma::find(
INZ.subvec(ind_i, cumsumstate(i) - 1));
if (ind.n_elem > 0) {
arma::vec gradIrow(numberOfStates(i), arma::fill::zeros);
for (unsigned int j = 0; j < numberOfStates(i); j++) {
double tmp = weights(i, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_i + j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(ind_i + j, 0);
}
arma::mat gradI(numberOfStates(i), numberOfStates(i), arma::fill::zeros);
gradI.eye();
gradI.each_row() -= init.subvec(ind_i, cumsumstate(i) - 1).t();
gradI.each_col() %= init.subvec(ind_i, cumsumstate(i) - 1);
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
for (unsigned int jj = 1; jj < numberOfStates.n_elem; jj++) {
unsigned int ind_jj = (cumsumstate(jj) - numberOfStates(jj));
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
if ((j >= ind_jj) & (j < cumsumstate(jj))) {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) += tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * (1.0 - weights(jj, k));
} else {
grad_k.subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) -= tmp
* beta(j, 0) * initk(j, k) * X.row(k).t() * weights(jj, k);
}
}
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll -= arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
}
}
}
if(error > 0){
ll = -arma::datum::inf;
grad.fill(-arma::datum::inf);
}
return List::create(Named("objective") = -ll, Named("gradient") = wrap(-grad));
}
List objective(const arma::mat& transition, NumericVector emissionArray,
const arma::vec& init, IntegerVector obsArray, const arma::imat& ANZ,
IntegerVector emissNZ, const arma::ivec& INZ, const arma::ivec& nSymbols, int threads) {
IntegerVector eDims = emissionArray.attr("dim"); //m,p,r
IntegerVector oDims = obsArray.attr("dim"); //k,n,r
arma::cube emission(emissionArray.begin(), eDims[0], eDims[1], eDims[2], false, true);
arma::icube obs(obsArray.begin(), oDims[0], oDims[1], oDims[2], false, true);
arma::icube BNZ(emissNZ.begin(), emission.n_rows, emission.n_cols - 1, emission.n_slices, false, true);
arma::vec grad(arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ), arma::fill::zeros);
// arma::cube alpha(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
// arma::cube beta(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
// arma::mat scales(obs.n_cols, obs.n_slices); //m,n,k
//
// internalForward(transition, emission, init, obs, alpha, scales, threads);
// if (!scales.is_finite()) {
// grad.fill(-arma::math::inf());
// return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
// }
//
// internalBackward(transition, emission, obs, beta, scales, threads);
// if (!beta.is_finite()) {
// grad.fill(-arma::math::inf());
// return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
// }
//use this instead of local vectors with grad += grad_k;, uses more memory but gives bit-identical results
//arma::mat gradmat(arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ), obs.n_slices);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(none) shared(grad, nSymbols, ANZ, BNZ, INZ, obs, init, transition, emission, error)
for (int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, init, obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
arma::vec gradArow(emission.n_rows);
arma::mat gradA(emission.n_rows, emission.n_rows);
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(ANZ.row(i));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(i);
gradA.each_col() %= transition.row(i).t();
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, t + 1, k), r);
}
gradArow(j) += alpha(i, t) * tmp * beta(j, t + 1) / scales(t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += init(i) * tmp * beta(i, 0) / scales(0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp
* beta(i, t + 1) / scales(t + 1);
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
// InitProbs
arma::uvec ind = arma::find(INZ);
if (ind.n_elem > 0) {
arma::vec gradIrow(emission.n_rows);
arma::mat gradI(emission.n_rows, emission.n_rows);
gradIrow.zeros();
gradI.zeros();
gradI.eye();
gradI.each_row() -= init.t();
gradI.each_col() %= init;
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(j, 0) / scales(0);
}
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll += arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
// gradmat.col(k) = grad_k;
}
// for (unsigned int ii = 0; ii < grad_k.n_elem; ii++) {
// #pragma omp atomic
// grad(ii) += grad_k(ii);
// }
}
}
if(error > 0){
ll = -arma::math::inf();
grad.fill(-arma::math::inf());
}
// } else {
// grad = sum(gradmat, 1);
// }
return List::create(Named("objective") = -ll, Named("gradient") = wrap(-grad));
}
// [[Rcpp::export]]
Rcpp::List objective(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, arma::ucube& obs, const arma::umat& ANZ,
const arma::ucube& BNZ, const arma::uvec& INZ, const arma::uvec& nSymbols, unsigned int threads) {
arma::vec grad(arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ), arma::fill::zeros);
unsigned int error = 0;
double ll = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:ll) num_threads(threads) \
default(shared) //shared(grad, nSymbols, ANZ, BNZ, INZ, obs, init, transition, emission, error, arma::fill::zeros)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n
arma::vec scales(obs.n_cols); //n
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, init, obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
int countgrad = 0;
arma::vec grad_k(grad.n_elem, arma::fill::zeros);
// transitionMatrix
arma::vec gradArow(emission.n_rows);
arma::mat gradA(emission.n_rows, emission.n_rows);
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(ANZ.row(i));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(i);
gradA.each_col() %= transition.row(i).t();
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, t + 1, k), r);
}
gradArow(j) += alpha(i, t) * tmp * beta(j, t + 1);
}
}
gradArow = gradA * gradArow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (unsigned int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += init(i) * tmp * beta(i, 0);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = 1.0;
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.col(t), transition.col(i)) * tmp
* beta(i, t + 1);
}
}
}
gradBrow = gradB * gradBrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
// InitProbs
arma::uvec ind = arma::find(INZ);
if (ind.n_elem > 0) {
arma::vec gradIrow(emission.n_rows);
arma::mat gradI(emission.n_rows, emission.n_rows);
gradIrow.zeros();
gradI.zeros();
gradI.eye();
gradI.each_row() -= init.t();
gradI.each_col() %= init;
for (unsigned int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(j, 0);
}
gradIrow = gradI * gradIrow;
grad_k.subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
if (!scales.is_finite() || !beta.is_finite()) {
#pragma omp atomic
error++;
} else {
ll -= arma::sum(log(scales));
#pragma omp critical
grad += grad_k;
// gradmat.col(k) = grad_k;
}
// for (unsigned int ii = 0; ii < grad_k.n_elem; ii++) {
// #pragma omp atomic
// grad(ii) += grad_k(ii);
// }
}
}
if(error > 0){
ll = -arma::datum::inf;
grad.fill(-arma::datum::inf);
}
// } else {
// grad = sum(gradmat, 1);
// }
return Rcpp::List::create(Rcpp::Named("objective") = -ll, Rcpp::Named("gradient") = Rcpp::wrap(-grad));
}
List objectivex(const arma::mat& transition, NumericVector emissionArray,
const arma::vec& init, IntegerVector obsArray, const arma::imat& ANZ,
IntegerVector emissNZ, const arma::ivec& INZ, const arma::ivec& nSymbols,
const arma::mat& coef, const arma::mat& X, arma::ivec& numberOfStates,
int threads) {
IntegerVector eDims = emissionArray.attr("dim"); //m,p,r
IntegerVector oDims = obsArray.attr("dim"); //k,n,r
arma::cube emission(emissionArray.begin(), eDims[0], eDims[1], eDims[2], false, true);
arma::icube obs(obsArray.begin(), oDims[0], oDims[1], oDims[2], false, true);
arma::icube BNZ(emissNZ.begin(), emission.n_rows, emission.n_cols - 1, emission.n_slices, false, true);
unsigned int q = coef.n_rows;
arma::vec grad(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
arma::fill::zeros);
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
arma::cube alpha(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
arma::cube beta(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
arma::mat scales(obs.n_cols, obs.n_slices); //m,n,k
arma::sp_mat sp_trans(transition);
internalForwardx(sp_trans.t(), emission, initk, obs, alpha, scales, threads);
if (!scales.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
internalBackwardx(sp_trans, emission, obs, beta, scales, threads);
if (!beta.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
arma::ivec cumsumstate = arma::cumsum(numberOfStates);
arma::mat gradmat(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
obs.n_slices, arma::fill::zeros);
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) num_threads(threads) \
default(none) shared(q, alpha, beta, scales, gradmat, nSymbols, ANZ, BNZ, INZ, \
numberOfStates, cumsumstate, obs, init, initk, X, weights, transition, emission)
for (int k = 0; k < obs.n_slices; k++) {
int countgrad = 0;
// transitionMatrix
if (arma::accu(ANZ) > 0) {
for (int jj = 0; jj < numberOfStates.n_elem; jj++) {
arma::vec gradArow(numberOfStates(jj));
arma::mat gradA(numberOfStates(jj), numberOfStates(jj));
int ind_jj = cumsumstate(jj) - numberOfStates(jj);
for (int i = 0; i < numberOfStates(jj); i++) {
arma::uvec ind = arma::find(ANZ.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1);
gradA.each_col() %= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1).t();
for (int j = 0; j < numberOfStates(jj); j++) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(ind_jj + i, t, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_jj + j, obs(r, t + 1, k), r);
}
gradArow(j) += tmp * beta(ind_jj + j, t + 1, k) / scales(t + 1, k);
}
}
gradArow = gradA * gradArow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(BNZ) > 0) {
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = initk(i, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += tmp * beta(i, 0, k) / scales(0, k);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = beta(i, t + 1, k) / scales(t + 1, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.slice(k).col(t), transition.col(i)) * tmp;
}
}
}
gradBrow = gradB * gradBrow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(INZ) > 0) {
for (int i = 0; i < numberOfStates.n_elem; i++) {
int ind_i = cumsumstate(i) - numberOfStates(i);
arma::uvec ind = arma::find(
INZ.subvec(ind_i, cumsumstate(i) - 1));
if (ind.n_elem > 0) {
arma::vec gradIrow(numberOfStates(i), arma::fill::zeros);
for (int j = 0; j < numberOfStates(i); j++) {
double tmp = weights(i, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_i + j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(ind_i + j, 0, k) / scales(0, k);
}
arma::mat gradI(numberOfStates(i), numberOfStates(i), arma::fill::zeros);
gradI.eye();
gradI.each_row() -= init.subvec(ind_i, cumsumstate(i) - 1).t();
gradI.each_col() %= init.subvec(ind_i, cumsumstate(i) - 1);
gradIrow = gradI * gradIrow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
for (int jj = 1; jj < numberOfStates.n_elem; jj++) {
int ind_jj = (cumsumstate(jj) - numberOfStates(jj));
for (int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
if ((j >= ind_jj) & (j < cumsumstate(jj))) {
gradmat.col(k).subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) += tmp
* beta(j, 0, k) / scales(0, k) * initk(j, k) * X.row(k).t() * (1.0 - weights(jj, k));
} else {
gradmat.col(k).subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) -= tmp
* beta(j, 0, k) / scales(0, k) * initk(j, k) * X.row(k).t() * weights(jj, k);
}
}
}
}
return List::create(Named("objective") = -arma::accu(log(scales)),
Named("gradient") = wrap(-sum(gradmat, 1)));
}
// [[Rcpp::export]]
Rcpp::List EMx(const arma::mat& transition_, const arma::cube& emission_, const arma::vec& init_,
const arma::ucube& obs, const arma::uvec& nSymbols, const arma::mat& coef_, const arma::mat& X,
const arma::uvec& numberOfStates, int itermax, double tol, int trace, unsigned int threads) {
// Make sure we don't alter the original vec/mat/cube
// needed for cube, in future maybe in other cases as well
arma::cube emission(emission_);
arma::mat transition(transition_);
arma::vec init(init_);
arma::mat coef(coef_);
coef.col(0).zeros();
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
return Rcpp::List::create(Rcpp::Named("error") = 3);
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
//
// //EM-algorithm begins
//
double change = tol + 1.0;
int iter = 0;
arma::uvec cumsumstate = arma::cumsum(numberOfStates);
double sumlogLik_new = 0;
double sumlogLik = -1e150;
while ((change > tol) & (iter < itermax)) {
iter++;
arma::mat ksii(emission.n_rows, emission.n_rows, arma::fill::zeros);
arma::cube gamma(emission.n_rows, emission.n_cols, emission.n_slices, arma::fill::zeros);
arma::vec delta(emission.n_rows, arma::fill::zeros);
arma::mat bsi(emission.n_rows, obs.n_slices);
sumlogLik_new = 0;
double max_sf = 1;
unsigned int error_code = 0;
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) reduction(+:sumlogLik_new) num_threads(threads) \
default(shared) //shared(bsi, initk, transition, obs, emission, delta, ksii, gamma, nSymbols, error_code, max_sf, arma::fill::zeros)
for (unsigned int k = 0; k < obs.n_slices; k++) {
if (error_code == 0) {
arma::mat alpha(emission.n_rows, obs.n_cols); //m,n,k
arma::vec scales(obs.n_cols);
arma::sp_mat sp_trans(transition);
uvForward(sp_trans.t(), emission, initk.col(k), obs.slice(k), alpha, scales);
arma::mat beta(emission.n_rows, obs.n_cols); //m,n,k
uvBackward(sp_trans, emission, obs.slice(k), beta, scales);
sumlogLik_new -= arma::sum(log(scales));
arma::mat ksii_k(emission.n_rows, emission.n_rows, arma::fill::zeros);
arma::cube gamma_k(emission.n_rows, emission.n_cols, emission.n_slices, arma::fill::zeros);
arma::vec delta_k(emission.n_rows);
delta_k = alpha.col(0) % beta.col(0) / scales(0);
for (unsigned int i = 0; i < emission.n_rows; i++) {
for (unsigned int j = 0; j < emission.n_rows; j++) {
if (transition(i, j) > 0.0) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(i, t) * transition(i, j) * beta(j, t + 1);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, t + 1, k), r);
}
ksii_k(i, j) += tmp;
}
}
}
}
for (unsigned int r = 0; r < emission.n_slices; r++) {
for (unsigned int l = 0; l < nSymbols(r); l++) {
for (unsigned int i = 0; i < emission.n_rows; i++) {
if (emission(i, l, r) > 0.0) {
for (unsigned int t = 0; t < obs.n_cols; t++) {
if (l == (obs(r, t, k))) {
double tmp = alpha(i, t) * beta(i, t) / scales(t);
gamma_k(i, l, r) += tmp;
}
}
}
}
}
}
for (unsigned int j = 0; j < emission.n_rows; j++) {
bsi(j, k) = beta(j, 0) * initk(j, k);
}
#pragma omp critical
{
if(!scales.is_finite()) {
error_code = 1;
}
if(!beta.is_finite()) {
error_code = 2;
}
max_sf = std::min(max_sf, scales.max());
delta += delta_k;
ksii += ksii_k;
gamma += gamma_k;
}
}
}
if(error_code == 1) {
return Rcpp::List::create(Rcpp::Named("error") = 1);
}
if(error_code == 2) {
return Rcpp::List::create(Rcpp::Named("error") = 2);
}
if (max_sf > 1e150) {
Rcpp::warning("Largest scaling factor was %e, results can be numerically unstable.", max_sf);
}
change = (sumlogLik_new - sumlogLik) / (std::abs(sumlogLik) + 0.1);
sumlogLik = sumlogLik_new;
if (trace > 0) {
if(iter == 0) {
Rcpp::Rcout << "Log-likelihood of initial model: " << sumlogLik << std::endl;
} else {
if (trace > 1) {
Rcpp::Rcout << "iter: " << iter;
Rcpp::Rcout << " logLik: " << sumlogLik;
Rcpp::Rcout << " relative change: " << change << std::endl;
}
}
}
if (change > tol) {
unsigned int error = optCoef(weights, obs, emission, bsi, coef, X, cumsumstate,
numberOfStates, trace);
if (error != 0) {
return Rcpp::List::create(Rcpp::Named("error") = error);
}
if (obs.n_cols > 1) {
ksii.each_col() /= sum(ksii, 1);
transition = ksii;
}
for (unsigned int r = 0; r < emission.n_slices; r++) {
gamma.slice(r).cols(0, nSymbols(r) - 1).each_col() /= sum(
gamma.slice(r).cols(0, nSymbols(r) - 1), 1);
emission.slice(r).cols(0, nSymbols(r) - 1) = gamma.slice(r).cols(0, nSymbols(r) - 1);
}
for (unsigned int i = 0; i < numberOfStates.n_elem; i++) {
delta.subvec(cumsumstate(i) - numberOfStates(i), cumsumstate(i) - 1) /= arma::as_scalar(
arma::accu(delta.subvec(cumsumstate(i) - numberOfStates(i), cumsumstate(i) - 1)));
}
init = delta;
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
}
}
if (trace > 0) {
if (iter == itermax) {
Rcpp::Rcout << "EM algorithm stopped after reaching the maximum number of " << iter
<< " iterations." << std::endl;
} else {
Rcpp::Rcout << "EM algorithm stopped after reaching the relative change of " << change;
Rcpp::Rcout << " after " << iter << " iterations." << std::endl;
}
Rcpp::Rcout << "Final log-likelihood: " << sumlogLik << std::endl;
}
return Rcpp::List::create(Rcpp::Named("coefficients") = Rcpp::wrap(coef), Rcpp::Named("initialProbs") = Rcpp::wrap(init),
Rcpp::Named("transitionMatrix") = Rcpp::wrap(transition), Rcpp::Named("emissionArray") = Rcpp::wrap(emission),
Rcpp::Named("logLik") = sumlogLik, Rcpp::Named("iterations") = iter, Rcpp::Named("change") = change,
Rcpp::Named("error") = 0);
}