// [[Rcpp::export]]
arma::mat BeQTL2(const arma::mat & A, const arma::mat & B, const arma::umat & Bootmat){
  int bsi= Bootmat.n_rows;
  arma::mat C(A.n_cols*B.n_cols,Bootmat.n_rows);
  arma::mat tC(A.n_rows,B.n_rows);
  for(int i=0; i<bsi; i++){
    tC = cor(A.rows(Bootmat.row(i)),B.rows(Bootmat.row(i)));
    C.col(i) = vectorise(tC,0);
  }
  C.elem(find_nonfinite(C)).zeros();

  return reshape(median(C,1),A.n_cols,B.n_cols);
}
//Script that takes two matrices, performs bootstrapped correlation, and returns the median
// [[Rcpp::export]]
arma::mat BeQTL(const arma::mat & A, const arma::mat & B, const arma::umat & Bootmat){
  int bsi= Bootmat.n_rows;
  Rcpp::Rcout<<"Starting Bootstrap!"<<std::endl;
  arma::mat C(A.n_cols*B.n_cols,Bootmat.n_rows);
  arma::mat tA(A.n_rows,A.n_cols);
  arma::mat tB(B.n_rows,B.n_cols);
  arma::mat tC(A.n_rows,B.n_rows);
  for(int i=0; i<bsi; i++){
    tA = A.rows(Bootmat.row(i));
    tB = B.rows(Bootmat.row(i));
    tC = cor(tA,tB);
    C.col(i) = vectorise(tC,0);
  }
  C.elem(find_nonfinite(C)).zeros();

 return reshape(median(C,1),A.n_cols,B.n_cols);
}
Example #3
0
// bootstrap class
Boot::Boot(const Data& data, Estimator* estimator, const arma::umat& rep)
  : data(data), n(data.n), p(data.p), rep(rep), r(rep.n_cols) {

  coef.set_size(p, r);
  fitted.set_size(n, r);
  resid.set_size(n, r);
  scale.set_size(1, r);

  arma::uvec indices;

  Data resamp;

  // for each replicate, construct the dataset then estimate
  for (int i = 0; i < r; i++) {
    indices = rep.col(i);
    resamp.x = data.x.rows(indices);
    resamp.y = data.y.elem(indices);
    (*estimator)(resamp, coef.colptr(i), fitted.colptr(i), resid.colptr(i),
                 scale.colptr(i));
  }
}
Example #4
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));
}
Example #5
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));
}
Example #6
0
double ung_ssm::bsf_filter(const unsigned int nsim, arma::cube& alpha,
  arma::mat& weights, arma::umat& indices) {
  
  arma::uvec nonzero = arma::find(P1.diag() > 0);
  arma::mat L_P1(m, m, arma::fill::zeros);
  if (nonzero.n_elem > 0) {
    L_P1.submat(nonzero, nonzero) =
      arma::chol(P1.submat(nonzero, nonzero), "lower");
  }
  std::normal_distribution<> normal(0.0, 1.0);
  for (unsigned int i = 0; i < nsim; i++) {
    arma::vec um(m);
    for(unsigned int j = 0; j < m; j++) {
      um(j) = normal(engine);
    }
    alpha.slice(i).col(0) = a1 + L_P1 * um;
  }
  
  std::uniform_real_distribution<> unif(0.0, 1.0);
  arma::vec normalized_weights(nsim);
  double loglik = 0.0;
  
  if(arma::is_finite(y(0))) {
    weights.col(0) = log_obs_density(0, alpha);
    double max_weight = weights.col(0).max();
    weights.col(0) = arma::exp(weights.col(0) - max_weight);
    double sum_weights = arma::accu(weights.col(0));
    if(sum_weights > 0.0){
      normalized_weights = weights.col(0) / sum_weights;
    } else {
      return -std::numeric_limits<double>::infinity();
    }
    loglik = max_weight + std::log(sum_weights / nsim);
  } else {
    weights.col(0).ones();
    normalized_weights.fill(1.0 / nsim);
  }
  for (unsigned int t = 0; t < n; t++) {
    
    arma::vec r(nsim);
    for (unsigned int i = 0; i < nsim; i++) {
      r(i) = unif(engine);
    }
    
    indices.col(t) = stratified_sample(normalized_weights, r, nsim);
    
    arma::mat alphatmp(m, nsim);
    
    for (unsigned int i = 0; i < nsim; i++) {
      alphatmp.col(i) = alpha.slice(indices(i, t)).col(t);
    }
    
    for (unsigned int i = 0; i < nsim; i++) {
      arma::vec uk(k);
      for(unsigned int j = 0; j < k; j++) {
        uk(j) = normal(engine);
      }
      alpha.slice(i).col(t + 1) = C.col(t * Ctv) +
        T.slice(t * Ttv) * alphatmp.col(i) + R.slice(t * Rtv) * uk;
    }
    
    if ((t < (n - 1)) && arma::is_finite(y(t + 1))) {
      weights.col(t + 1) = log_obs_density(t + 1, alpha);
      
      double max_weight = weights.col(t + 1).max();
      weights.col(t + 1) = arma::exp(weights.col(t + 1) - max_weight);
      double sum_weights = arma::accu(weights.col(t + 1));
      if(sum_weights > 0.0){
        normalized_weights = weights.col(t + 1) / sum_weights;
      } else {
        return -std::numeric_limits<double>::infinity();
      }
      loglik += max_weight + std::log(sum_weights / nsim);
    } else {
      weights.col(t + 1).ones();
      normalized_weights.fill(1.0/nsim);
    }
  }
  // constant part of the log-likelihood
  switch(distribution) {
  case 0 :
    loglik += arma::uvec(arma::find_finite(y)).n_elem * norm_log_const(phi);
    break;
  case 1 : {
      arma::uvec finite_y(find_finite(y));
      loglik += poisson_log_const(y(finite_y), u(finite_y));
    } break;
  case 2 : {
    arma::uvec finite_y(find_finite(y));
    loglik += binomial_log_const(y(finite_y), u(finite_y));
  } break;
  case 3 : {
    arma::uvec finite_y(find_finite(y));
    loglik += negbin_log_const(y(finite_y), u(finite_y), phi);
  } break;
  }
  return loglik;
}
Example #7
0
double ung_ssm::psi_filter(const ugg_ssm& approx_model,
  const double approx_loglik, const arma::vec& scales,
  const unsigned int nsim, arma::cube& alpha, arma::mat& weights,
  arma::umat& indices) {
  
  arma::mat alphahat(m, n + 1);
  arma::cube Vt(m, m, n + 1);
  arma::cube Ct(m, m, n + 1);
  approx_model.smoother_ccov(alphahat, Vt, Ct);
  conditional_cov(Vt, Ct);
  
  std::normal_distribution<> normal(0.0, 1.0);
  
  
  for (unsigned int i = 0; i < nsim; i++) {
    arma::vec um(m);
    for(unsigned int j = 0; j < m; j++) {
      um(j) = normal(engine);
    }
    alpha.slice(i).col(0) = alphahat.col(0) + Vt.slice(0) * um;
  }
  
  std::uniform_real_distribution<> unif(0.0, 1.0);
  arma::vec normalized_weights(nsim);
  double loglik = 0.0;
  if(arma::is_finite(y(0))) {
    weights.col(0) = arma::exp(log_weights(approx_model, 0, alpha) - scales(0));
    double sum_weights = arma::accu(weights.col(0));
    if(sum_weights > 0.0){
      normalized_weights = weights.col(0) / sum_weights;
    } else {
      return -std::numeric_limits<double>::infinity();
    }
    loglik = approx_loglik + std::log(sum_weights / nsim);
  } else {
    weights.col(0).ones();
    normalized_weights.fill(1.0 / nsim);
    loglik = approx_loglik;
  }
  
  for (unsigned int t = 0; t < n; t++) {
    arma::vec r(nsim);
    for (unsigned int i = 0; i < nsim; i++) {
      r(i) = unif(engine);
    }
    indices.col(t) = stratified_sample(normalized_weights, r, nsim);
    
    arma::mat alphatmp(m, nsim);
    
    // for (unsigned int i = 0; i < nsim; i++) {
    //   alphatmp.col(i) = alpha.slice(i).col(t);
    // }
    for (unsigned int i = 0; i < nsim; i++) {
      alphatmp.col(i) = alpha.slice(indices(i, t)).col(t);
      //alpha.slice(i).col(t) = alphatmp.col(indices(i, t));
    }
    for (unsigned int i = 0; i < nsim; i++) {
      arma::vec um(m);
      for(unsigned int j = 0; j < m; j++) {
        um(j) = normal(engine);
      }
      alpha.slice(i).col(t + 1) = alphahat.col(t + 1) +
        Ct.slice(t + 1) * (alphatmp.col(i) - alphahat.col(t)) + Vt.slice(t + 1) * um;
    }
    
    if ((t < (n - 1)) && arma::is_finite(y(t + 1))) {
      weights.col(t + 1) =
        arma::exp(log_weights(approx_model, t + 1, alpha) - scales(t + 1));
      double sum_weights = arma::accu(weights.col(t + 1));
      if(sum_weights > 0.0){
        normalized_weights = weights.col(t + 1) / sum_weights;
      } else {
        return -std::numeric_limits<double>::infinity();
      }
      loglik += std::log(sum_weights / nsim);
    } else {
      weights.col(t + 1).ones();
      normalized_weights.fill(1.0 / nsim);
    }
  }
  return loglik;
}