void HDP::sample_first_level_concentration(double gamma_a, double gamma_b) {
/// (p 585 in escobar and west)
double shape = gamma_a;
double scale = gamma_b;
int n = 0;
RNGScope scope;
for (int k = 0; k < hdp_state_->num_topics_; ++k) {
n += hdp_state_->beta_u_[k];
}
double eta = Rf_rbeta(hdp_state_->gamma_ + 1, n);
double pi = shape + hdp_state_->num_topics_ - 1;
double rate = 1.0 / scale - log(eta);
pi = pi / (pi + rate * n);
unsigned int cc = Rf_rbinom(1,pi);
if (cc == 1)
hdp_state_->gamma_ = Rf_rgamma(shape + hdp_state_->num_topics_, 1.0 / rate);
else
hdp_state_->gamma_ = Rf_rgamma(shape + hdp_state_->num_topics_ - 1, 1.0 / rate);
}
void HDP::sample_top_level_proportions() {
double total = 0;
RNGScope scope;
for (int k = 0; k < hdp_state_->num_topics_; ++k) {
hdp_state_->pi_[k] = Rf_rgamma(hdp_state_->beta_u_[k], 1.0);
total += hdp_state_->pi_[k];
}
hdp_state_->pi_left_ = Rf_rgamma(hdp_state_->gamma_, 1.0);
total += hdp_state_->pi_left_;
for (int k = 0; k < hdp_state_->num_topics_; ++k) {
hdp_state_->pi_[k] /= total;
}
hdp_state_->pi_left_ /= total;
double etaW = hdp_state_->size_vocab_ * hdp_state_->eta_;
smoothing_prob_sum_ = 0.0;
for (int k = 0; k < hdp_state_->num_topics_; ++k) {
smoothing_prob_[k] = hdp_state_->alpha_ * hdp_state_->pi_[k] / (hdp_state_->word_counts_by_topic_[k] + etaW);
smoothing_prob_sum_ += smoothing_prob_[k];
}
}
// [[Rcpp::interfaces(cpp)]]
arma::rowvec dir(arma::rowvec a)
{
int l=a.n_cols;
arma::rowvec x(l);
GetRNGstate();
for (int i=0;i<l;i++){
x[i]=Rf_rgamma(a[i],1);
}
PutRNGstate();
double sm=sum(x);
return x/sm;
}
void HDP::sample_second_level_concentration(double alpha_a, double alpha_b) {
double shape = alpha_a;
double scale = alpha_b;
RNGScope scope;
int n = 0;
for (int k = 0; k < hdp_state_->num_topics_; ++k) {
n += hdp_state_->beta_u_[k];
}
double rate, sum_log_w, sum_s;
for (int step = 0; step < 20; ++step) {
sum_log_w = 0.0;
sum_s = 0.0;
for (int d = 0; d < num_docs_; ++d) {
sum_log_w += log(Rf_rbeta(hdp_state_->alpha_ + 1, doc_states_[d]->doc_length_));
sum_s += (double)Rf_rbinom(1,doc_states_[d]->doc_length_ / (doc_states_[d]->doc_length_ + hdp_state_->alpha_));
}
rate = 1.0 / scale - sum_log_w;
hdp_state_->alpha_ = Rf_rgamma(shape + n - sum_s, 1.0 / rate);
}
}
Type rgamma(Type shape, Type scale)
{
return Rf_rgamma(asDouble(shape), asDouble(scale));
}
// [[Rcpp::export]]
Rcpp::NumericVector bayes_lm_rcpp_arma_(int n,
int p,
int nsamp,
double prop_nonzero,
double true_beta_sd,
double true_sigma,
double sd_x,
bool print_stats,
bool write_samples,
Rcpp::CharacterVector samples_file_loc,
char decomp_method) {
// Declare model data structures -----------------------
arma::vec true_beta; // true coefficient vector
arma::vec y; // response values
arma::mat X; // predictor coefficient matrix
arma::vec beta; // current value of beta sample
double gamma; // current value of gamma sample
arma::mat Sigma_inv_0; // inverse of beta variance hyperparam
double nu_0; // hyperparam 1 for inverse-gamma prior
double sigma_sq_0; // hyperparam 2 for inverse-gamma prior
arma::mat out_beta; // memory for beta samples
arma::vec out_gamma; // memory for gamma samples
// Declare storage and timer data structures -----------
std::ofstream ctime_file; // sampler loop computational time file
std::ofstream samples_file; // samples file
struct timespec start[3]; // store event starting time information
struct timespec finish[3]; // store event ending time information
double elapsed[3] = { 0, 0, 0 }; // tracks event cumulative elapsed time
arma::vec::iterator curr; // iterator steps through current val
arma::vec::iterator end; // iterator to mark one past the last val
// Set values of model objects -------------------------
// Set values of beta
true_beta = sample_beta(p, prop_nonzero, true_beta_sd);
// Sample data
X.randn(n, p);
X *= sd_x;
y = (X * true_beta) + (true_sigma * arma::vec(n, arma::fill::randn));
/* Set the priors; see Hoff pgs. 154-155 for the meanings of the priors.
* Note: we are implicitely specifying the mean hyperparameter for beta to
* be 0 by ommitting the term in the Gibbs sampler conditional mean
* calculation.
*/
Sigma_inv_0.eye(p, p);
nu_0 = 1;
sigma_sq_0 = 1;
// Write param vals to file ----------------------------
// Write true values of beta, sigma^{-2} to the first row of output file
if (write_samples) {
samples_file.open(samples_file_loc[0].begin());
curr = true_beta.begin();
end = true_beta.end();
for ( ; (curr != end); curr++) {
samples_file << *curr << " ";
}
samples_file << 1 / (true_sigma * true_sigma) << "\n";
samples_file.close();
}
// Preliminary calculations ----------------------------
arma::mat tXX; // value of X^{T} X
arma::vec tXy; // value of X^{T} y
double shapeval; // shape parameter for gamma distribution samples
double nu_sigma_sq_0; // product of nu_0 and sigma^2_0
tXX = X.t() * X;
tXy = X.t() * y;
nu_sigma_sq_0 = nu_0 * sigma_sq_0;
shapeval = (nu_0 + n) / 2;
// Sampler loop ----------------------------------------
arma::mat V; // variance of current beta sample
arma::vec m; // mean of current beta sample
arma::vec err; // model error, i.e. y - X \beta
double root_SSR; // square root of SSR
double SSR; // SSR (sum of squared errors)
double scaleval; // scale parameter for gamma distribution samples
// Set pointer to desired multivariate normal sampling function
arma::vec (*samp_mvnorm)(arma::vec&, arma::mat&);
switch (decomp_method) {
case 'c':
samp_mvnorm = &mvrnorm_chol;
break;
case 'e':
samp_mvnorm = &mvrnorm_eigen;
break;
default:
throw std::runtime_error("Illegal value of decomp_method");
}
// Conditionally allocate memory for samples
if (print_stats) {
out_beta.set_size(p, nsamp);
out_gamma.set_size(nsamp);
}
// Conditionally open samples file stream
if (write_samples) {
samples_file.open(samples_file_loc[0].begin(), std::fstream::app);
}
// Clock timer objects and initialization; requires POSIX system
CLOCK_START(OVERALL);
// Initial value for gamma
gamma = 1;
for (int s = 0; s < nsamp; s++) {
// Sample beta
CLOCK_START(INVERSE)
V = inv_sympd(Sigma_inv_0 + (gamma * tXX));
CLOCK_STOP(INVERSE);
m = gamma * V * tXy;
CLOCK_START(SAMP_NORM)
beta = samp_mvnorm(m, V);
CLOCK_STOP(SAMP_NORM);
// Sample gamma
err = y - (X * beta);
root_SSR = norm(err);
SSR = root_SSR * root_SSR;
scaleval = 2 / (nu_sigma_sq_0 + SSR);
gamma = Rf_rgamma(shapeval, scaleval);
// Conditionally store data in memory / write to file
if (write_samples) {
curr = beta.begin();
end = beta.end();
for ( ; (curr != end); curr++) {
samples_file << *curr << " ";
}
samples_file << gamma << "\n";
}
if (print_stats) {
out_beta.col(s) = beta;
out_gamma(s) = gamma;
}
// Allow user to interrupt and return to the R REPL
if (s % 1000 == 0) {
Rcpp::checkUserInterrupt();
}
}
// Calculate elapsed time
CLOCK_STOP(OVERALL);
// Print summary statistics ----------------------------
if (print_stats) {
// Create tables with true values and empirical quantiles
arma::mat table_beta_quant;
arma::mat table_gamma_quant;
// Declare and initialize probs, true_gamma
arma::vec probs;
arma::vec true_gamma;
probs << 0.025 << 0.500 << 0.975;
true_gamma << 1 / (true_sigma * true_sigma);
// Calculate empirical quantiles
out_beta = out_beta.t();
table_beta_quant = quantile_table(true_beta, out_beta, probs);
table_gamma_quant = quantile_table(true_gamma, out_gamma, probs);
Rcpp::Rcout << "\n"
<< "Parameter specifications:\n"
<< "-------------------------\n"
<< "n: " << n << "\n"
<< "p: " << p << "\n"
<< "prop_nonzero: " << prop_nonzero << "\n"
<< "true_beta_sd: " << true_beta_sd << "\n"
<< "true_sigma: " << true_sigma << "\n"
<< "sd_x: " << sd_x << "\n"
<< "nsamp: " << nsamp << "\n"
<< "print_stats: " << print_stats << "\n"
<< "write_samples: " << write_samples << "\n"
<< "samples_file_loc: " << samples_file_loc << "\n"
<< "decomp_method: " << decomp_method << "\n";
Rcpp::Rcout << "\n"
<< "Elapsed time:\n"
<< "-------------\n"
<< "Inverse: " << elapsed[INVERSE] << "\n"
<< "Sampling normal: " << elapsed[SAMP_NORM] << "\n"
<< "Overall: " << elapsed[OVERALL] << "\n"
<< "\n";
Rcpp::Rcout << "true beta 2.5% 50% 97.5%\n"
<< "------------------------------------\n"
<< table_beta_quant
<< "\n"
<< " true gam 2.5% 50% 97.5%\n"
<< "------------------------------------\n"
<< table_gamma_quant
<< "\n";
}
// Return computational time
return Rcpp::NumericVector::create(Rcpp::Named("inverse") = elapsed[INVERSE],
Rcpp::Named("mvnsamp") = elapsed[SAMP_NORM],
Rcpp::Named("overall") = elapsed[OVERALL]);
}
