Exemple #1
0
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);
}
Exemple #2
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));
}
Exemple #3
0
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));
}
Exemple #4
0
// [[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));
}
Exemple #5
0
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)));
}
Exemple #6
0
// [[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);
}