inline
arma_warn_unused
typename T1::elem_type
sum(const Op<T1, op_sum>& in)
{
arma_extra_debug_sigprint();
arma_extra_debug_print("sum(): two consecutive sum() calls detected");
return accu(in.m);
}
double HMM<Distribution>::LogLikelihood(const arma::mat& dataSeq) const
{
arma::mat forward;
arma::vec scales;
Forward(dataSeq, scales, forward);
// The log-likelihood is the log of the scales for each time step.
return accu(log(scales));
}
::libmaus2::autoarray::AutoArray < std::pair<uint64_t,uint64_t> > computeSegAccu() const
{
::libmaus2::autoarray::AutoArray<uint64_t> preaccu(index.size()+1);
for ( uint64_t i = 0; i < index.size(); ++i )
preaccu[i] = index[i].size();
preaccu.prefixSums();
::libmaus2::autoarray::AutoArray < std::pair<uint64_t,uint64_t> > accu(index.size());
for ( uint64_t i = 1; i < preaccu.size(); ++i )
accu[i-1] = std::pair<uint64_t,uint64_t>(preaccu[i-1],preaccu[i]);
return accu;
}
// Posterior Density Function to sample Theta
double f_theta( colvec logTheta, colvec mTheta, mat Otheta, double Tau, mat Y, mat Fit, rowvec Sigma, double logEHRTime )
{
double prior, like, post;
colvec cTheta = ( logTheta - mTheta ) ;
prior = - 0.5 * Tau * as_scalar( cTheta.t() * Otheta * cTheta );
mat D = diagmat( 1 / Sigma );
like = - 0.5 * accu( pow ( log( Y ) - log( Fit ), 2 ) * D ); // Need to figure out what to do with Sigma
// Conditional Posterior -----------------------------------------------------------
post = prior + like + Rf_dnorm4( logEHRTime, 0, 1, 1 );
return post;
}
void SPF::update_shape(int user, int item, int rating) {
sp_fmat phi_SF = logtau.col(user) % data->ratings.col(item);
double phi_sum = accu(phi_SF);
fmat phi_MF;
float phi_B = 0;
// we don't need to do a similar check for factor only because
// sparse matrices play nice when empty
if (!settings->social_only) {
phi_MF = exp(logtheta.col(user) + logbeta.col(item));
phi_sum += accu(phi_MF);
}
if (settings->item_bias) {
phi_B = delta(item);
phi_sum += phi_B;
}
if (phi_sum == 0)
return;
if (!settings->factor_only & !settings->fix_influence) {
phi_SF /= phi_sum * rating;
int neighbor;
for (int n = 0; n < data->neighbor_count(user); n++) {
neighbor = data->get_neighbor(user, n);
a_tau(neighbor, user) += phi_SF(neighbor, 0);
}
}
if (!settings->social_only) {
phi_MF /= phi_sum * rating;
a_theta.col(user) += phi_MF;
a_beta_user.col(item) += phi_MF * scale;
}
if (settings->item_bias) {
a_delta(item) += (phi_B / (phi_sum * rating)) * scale;
}
}
/**
* Define the discrete distribution as having the given probabilities for each
* observation.
*
* @param probabilities Probabilities of each possible observation.
*/
DiscreteDistribution(const arma::vec& probabilities)
{
// We must be sure that our distribution is normalized.
double sum = accu(probabilities);
if (sum > 0)
this->probabilities = probabilities / sum;
else
{
this->probabilities.set_size(probabilities.n_elem);
this->probabilities.fill(1 / probabilities.n_elem);
}
}
double getPredictionAccuracy(mat& predictions, mat& labels){
int m = predictions.n_rows;
double accuracy = 0;
mat anticipations = round(predictions);
/* For each prediction */
for (int i = 0; i < m; i++){
/* If tere is no difference between rounded prediction and label*/
if (accu(labels.row(i) - anticipations.row(i)) == 0) accuracy += 1;
}
return (accuracy / m) * 100;
}
//' Samples from a Dirichlet distribution given a hyperparameter
//'
//' @param num_elements the dimention of the Dirichlet distribution
//' @param alpha the hyperparameter vector (a column vector)
//'
//' @return returns a Dirichlet sample (a column vector)
//'
//' @note
//' Author: Clint P. George
//'
//' Created on: 2014
//'
//' @family utils
//'
//' @export
// [[Rcpp::export]]
arma::vec sample_dirichlet(unsigned int num_elements, arma::vec alpha){
arma::vec dirichlet_sample = arma::zeros<arma::vec>(num_elements);
for ( register unsigned int i = 0; i < num_elements; i++ )
dirichlet_sample(i) = rgamma(1, alpha(i), 1.0)(0); // R::rgamma(1, alpha(i));
dirichlet_sample /= accu(dirichlet_sample);
return dirichlet_sample;
}
void HMM<Distribution>::Forward(const arma::mat& dataSeq,
arma::vec& scales,
arma::mat& forwardProb) const
{
// Our goal is to calculate the forward probabilities:
// P(X_k | o_{1:k}) for all possible states X_k, for each time point k.
forwardProb.zeros(transition.n_rows, dataSeq.n_cols);
scales.zeros(dataSeq.n_cols);
// The first entry in the forward algorithm uses the initial state
// probabilities. Note that MATLAB assumes that the starting state (at
// t = -1) is state 0; this is not our assumption here. To force that
// behavior, you could append a single starting state to every single data
// sequence and that should produce results in line with MATLAB.
for (size_t state = 0; state < transition.n_rows; state++)
forwardProb(state, 0) = initial(state) *
emission[state].Probability(dataSeq.unsafe_col(0));
// Then normalize the column.
scales[0] = accu(forwardProb.col(0));
forwardProb.col(0) /= scales[0];
// Now compute the probabilities for each successive observation.
for (size_t t = 1; t < dataSeq.n_cols; t++)
{
for (size_t j = 0; j < transition.n_rows; j++)
{
// The forward probability of state j at time t is the sum over all states
// of the probability of the previous state transitioning to the current
// state and emitting the given observation.
forwardProb(j, t) = accu(forwardProb.col(t - 1) %
trans(transition.row(j))) *
emission[j].Probability(dataSeq.unsafe_col(t));
}
// Normalize probability.
scales[t] = accu(forwardProb.col(t));
forwardProb.col(t) /= scales[t];
}
}
inline
arma_warn_unused
eT
mean(const subview_row<eT>& A)
{
arma_extra_debug_sigprint();
arma_debug_check( (A.n_elem == 0), "mean(): given object has no elements" );
const eT mu = accu(A) / eT(A.n_cols);
return is_finite(mu) ? mu : op_mean::direct_mean_robust(A);
}
inline
typename
enable_if2
<
(is_arma_sparse_type<T1>::value == true) && (resolves_to_sparse_vector<T1>::value == true),
typename T1::elem_type
>::result
sum(const T1& x)
{
arma_extra_debug_sigprint();
// sum elements
return accu(x);
}
void HMM<Distribution>::Forward(const arma::mat& dataSeq,
arma::vec& scales,
arma::mat& forwardProb) const
{
// Our goal is to calculate the forward probabilities:
// P(X_k | o_{1:k}) for all possible states X_k, for each time point k.
forwardProb.zeros(transition.n_rows, dataSeq.n_cols);
scales.zeros(dataSeq.n_cols);
// Starting state (at t = -1) is assumed to be state 0. This is what MATLAB
// does in their hmmdecode() function, so we will emulate that behavior.
for (size_t state = 0; state < transition.n_rows; state++)
forwardProb(state, 0) = transition(state, 0) *
emission[state].Probability(dataSeq.unsafe_col(0));
// Then normalize the column.
scales[0] = accu(forwardProb.col(0));
forwardProb.col(0) /= scales[0];
// Now compute the probabilities for each successive observation.
for (size_t t = 1; t < dataSeq.n_cols; t++)
{
for (size_t j = 0; j < transition.n_rows; j++)
{
// The forward probability of state j at time t is the sum over all states
// of the probability of the previous state transitioning to the current
// state and emitting the given observation.
forwardProb(j, t) = accu(forwardProb.col(t - 1) %
trans(transition.row(j))) *
emission[j].Probability(dataSeq.unsafe_col(t));
}
// Normalize probability.
scales[t] = accu(forwardProb.col(t));
forwardProb.col(t) /= scales[t];
}
}
sp_mat make_sample_basis(uint N,
uint K){
sp_mat basis = sp_mat(N,K);
set<uword> keys;
uvec samples = randi<uvec>(K,distr_param(0,N-1));
for(uint k = 0; k < K; k++){
while(keys.count(samples(k)) > 0){
samples(k) = randi<uvec>(1,distr_param(0,N-1))(0);
}
basis(samples(k),k) = 1;
keys.insert(samples(k));
}
assert(K == accu(basis));
return basis; // Should be orthonormal by default
}
//' A speedy sampling from a multimomial distribution
//'
//' @param theta a multinomial probability vector (K x 1 vector)
//'
//' @return returns a class index from [0, K)
//'
//' @note
//' Author: Clint P. George
//'
//' Created on: February 11, 2016
//'
//' @family utils
//'
//' @export
// [[Rcpp::export]]
unsigned int sample_multinomial (arma::vec theta) {
unsigned int t = 0;
double total_prob = accu(theta);
double u = runif(1)(0) * total_prob;
double cumulative_prob = theta(0);
while(u > cumulative_prob){
t++;
cumulative_prob += theta(t);
}
return t;
}
::libmaus2::autoarray::AutoArray< std::pair<uint64_t,uint64_t> > computeSegmentAccu()
{
uint64_t const numint = index.size();
::libmaus2::autoarray::AutoArray<uint64_t> preaccu(numint+1);
uint64_t k = 0;
for ( uint64_t i = 0; i < index.size(); ++i )
preaccu[k++] = index[i].size();
preaccu.prefixSums();
::libmaus2::autoarray::AutoArray< std::pair<uint64_t,uint64_t> > accu(numint);
for ( uint64_t i = 1; i < preaccu.size(); ++i )
accu[i-1] = std::pair<uint64_t,uint64_t>(
std::pair<uint64_t,uint64_t>(preaccu[i-1],preaccu[i])
);
return accu;
}
double Connectome::transitivity(const mat &W)
{
/*
Transitivity is the ratio of 'triangles to triplets' in the network.
(A classical version of the clustering coefficient).
Input: W weighted undirected connection matrix
Output: T transitivity scalar
Reference: Onnela et al. (2005) Phys Rev E 71:065103
*/
rowvec K = degree(W);
mat t = arma::pow(W,(1.0/3.0));
vec cyc3 = diagvec(t*t*t);
return accu(cyc3)/sum(K%(K-1));
}
static inline void
UpdateGradient(arma::mat& s,
const arma::mat& rrt,
const std::vector<MatrixType>& ais,
const arma::vec& bis,
const arma::vec& lambda,
const size_t lambdaOffset,
const double sigma)
{
for (size_t i = 0; i < ais.size(); ++i)
{
const double constraint = accu(ais[i] % rrt) - bis[i];
const double y = lambda[lambdaOffset + i] - sigma * constraint;
s -= y * ais[i];
}
}
inline
arma_warn_unused
typename T1::elem_type
sum
(
const T1& X,
const arma_empty_class junk1 = arma_empty_class(),
const typename enable_if< resolves_to_vector<T1>::value == true >::result* junk2 = 0
)
{
arma_extra_debug_sigprint();
arma_ignore(junk1);
arma_ignore(junk2);
return accu(X);
}
double HMM<Distribution>::Estimate(const arma::mat& dataSeq,
arma::mat& stateProb,
arma::mat& forwardProb,
arma::mat& backwardProb,
arma::vec& scales) const
{
// First run the forward-backward algorithm.
Forward(dataSeq, scales, forwardProb);
Backward(dataSeq, scales, backwardProb);
// Now assemble the state probability matrix based on the forward and backward
// probabilities.
stateProb = forwardProb % backwardProb;
// Finally assemble the log-likelihood and return it.
return accu(log(scales));
}
static inline void
UpdateObjective(double& objective,
const arma::mat& rrt,
const std::vector<MatrixType>& ais,
const arma::vec& bis,
const arma::vec& lambda,
const size_t lambdaOffset,
const double sigma)
{
for (size_t i = 0; i < ais.size(); ++i)
{
// Take the trace subtracted by the b_i.
const double constraint = accu(ais[i] % rrt) - bis[i];
objective -= (lambda[lambdaOffset + i] * constraint);
objective += (sigma / 2.) * constraint * constraint;
}
}
::libmaus2::autoarray::AutoArray< std::pair<uint64_t,uint64_t> > computeSymAccu()
{
uint64_t numint = 0;
for ( uint64_t i = 0; i < index.size(); ++i )
numint += index[i].size();
::libmaus2::autoarray::AutoArray<uint64_t> preaccu(numint+1);
uint64_t k = 0;
for ( uint64_t i = 0; i < index.size(); ++i )
for ( uint64_t j = 0; j < index[i].size(); ++j )
preaccu[k++] = index[i][j].vcnt;
preaccu.prefixSums();
::libmaus2::autoarray::AutoArray< std::pair<uint64_t,uint64_t> > accu(numint);
for ( uint64_t i = 1; i < preaccu.size(); ++i )
accu[i-1] = std::pair<uint64_t,uint64_t>(
std::pair<uint64_t,uint64_t>(preaccu[i-1],preaccu[i])
);
return accu;
}
/**
* Calculates the multivariate Gaussian probability density function for each
* data point (column) in the given matrix, with respect to the given mean and
* variance.
*
* @param x List of observations.
* @param mean Mean of multivariate Gaussian.
* @param cov Covariance of multivariate Gaussian.
* @param probabilities Output probabilities for each input observation.
*/
inline void phi(const arma::mat& x,
const arma::vec& mean,
const arma::mat& cov,
arma::vec& probabilities)
{
// Column i of 'diffs' is the difference between x.col(i) and the mean.
arma::mat diffs = x - (mean * arma::ones<arma::rowvec>(x.n_cols));
// Now, we only want to calculate the diagonal elements of (diffs' * cov^-1 *
// diffs). We just don't need any of the other elements. We can calculate
// the right hand part of the equation (instead of the left side) so that
// later we are referencing columns, not rows -- that is faster.
arma::mat rhs = -0.5 * inv(cov) * diffs;
arma::vec exponents(diffs.n_cols); // We will now fill this.
for (size_t i = 0; i < diffs.n_cols; i++)
exponents(i) = exp(accu(diffs.unsafe_col(i) % rhs.unsafe_col(i)));
probabilities = pow(2 * M_PI, (double) mean.n_elem / -2.0) *
pow(det(cov), -0.5) * exponents;
}
void BoxesSystem::update_state_and_particles(const mat& x_t, const mat& P_t, const mat& u_t, mat& x_tp1, mat& P_tp1) {
int M = P_t.n_cols;
x_tp1 = this->dynfunc(x_t, u_t);
// receive noisy measurement
mat z_tp1 = this->obsfunc(x_tp1, this->box_centers, sample_gaussian(zeros<mat>(N*R_DIM,1), .01*this->R));
mat W(M, 1, fill::zeros);
mat r(N*R_DIM, 1, fill::zeros);
// for each particle, weight by gauss_likelihood of that measurement given particle/agent observation
for(int m=0; m < M; ++m) {
mat z_particle = this->obsfunc(x_tp1, P_t.col(m), r);
mat e = z_particle - z_tp1;
W(m) = this->gauss_likelihood(e, this->R);
}
W = W / accu(W);
double sampling_noise = uniform(0, 1/double(M));
P_tp1 = this->low_variance_sampler(P_t, W, sampling_noise);
}
/*!
* \brief forward
* X: [N, C, 1, 1], usually the output of affine(fc) layer
* Y: [N, C, 1, 1], ground truth, with 1(true) or 0(false)
* \param[in] const vector<Blob*>& in in[0]:X, in[1]:Y
* \param[out] double& loss loss
* \param[out] Blob** out out: dX
*/
void SoftmaxLossLayer::go(const vector<shared_ptr<Blob>>& in,
double& loss,
shared_ptr<Blob>& dout,
int mode) {
//Blob X(*in[0]);
//Blob Y(*in[1]);
if (dout) {
dout.reset();
}
int N = in[0]->get_N();
int C = in[0]->get_C();
int H = in[0]->get_H();
int W = in[0]->get_W();
assert(H == 1 && W == 1);
mat mat_x = in[0]->reshape();
mat mat_y = in[1]->reshape();
/*! forward */
mat row_max = repmat(arma::max(mat_x, 1), 1, C);
mat_x = arma::exp(mat_x - row_max);
mat row_sum = repmat(arma::sum(mat_x, 1), 1, C);
mat e = mat_x / row_sum;
//e.print("e:\n");
//mat rrs = arma::sum(e, 1);
//rrs.print("rrs:\n");
mat prob = -arma::log(e);
//prob.print("prob:\n");
//(prob%mat_y).print("gg:\n");
/*! loss should near -log(1/C) */
loss = accu(prob % mat_y) / N;
/*! only forward */
if (mode == 1)
return;
/*! backward */
mat dx = e - mat_y;
dx /= N;
mat2Blob(dx, dout, (*in[0]).size());
return;
}
double GMM<FittingType>::LogLikelihood(
const arma::mat& data,
const std::vector<arma::vec>& meansL,
const std::vector<arma::mat>& covariancesL,
const arma::vec& weightsL) const
{
double loglikelihood = 0;
arma::vec phis;
arma::mat likelihoods(gaussians, data.n_cols);
for (size_t i = 0; i < gaussians; i++)
{
phi(data, meansL[i], covariancesL[i], phis);
likelihoods.row(i) = weightsL(i) * trans(phis);
}
// Now sum over every point.
for (size_t j = 0; j < data.n_cols; j++)
loglikelihood += log(accu(likelihoods.col(j)));
return loglikelihood;
}
long double TopicSearch::calc_lnTP_hybrid_multi_randomwalk(
size_t num_words,
vector <size_t> word_indices,
uvec Z_prime,
double random_walk_prob,
double multi_jump_prob) {
long double prob = 0.0;
long double multi_jump = 1.0;
vec beta_w;
for (size_t i = 0; i < num_words; i++){
beta_w = this->beta_counts_.col(this->word_ids_(word_indices[i]));
multi_jump *= beta_w(Z_prime(i)) / (accu(beta_w) + 1);
}
prob = random_walk_prob * multi_jump_prob * multi_jump
+ random_walk_prob * (1.0 - multi_jump_prob) * (long double)num_words
+ (1.0 - random_walk_prob) * num_words / (long double) this->num_topics_;
return log(prob + 1e-24);
}
// add_penalty to the target error 'terr'
void add_penalty(const unsigned int & i_e, vec & terr, const mat & W, const mat & H,
const unsigned int & N_non_missing, const vec & alpha, const vec & beta)
{
// add penalty term back to the loss function (terr)
if (alpha(0) != alpha(1))
terr(i_e) += 0.5*(alpha(0)-alpha(1))*accu(square(W))/N_non_missing;
if (beta(0) != beta(1))
terr(i_e) += 0.5*(beta(0)-beta(1))*accu(square(H))/N_non_missing;
if (alpha(1) != 0)
terr(i_e) += 0.5*alpha(1)*accu(W*W.t())/N_non_missing;
if (beta(1) != 0)
terr(i_e) += 0.5*beta(1)*accu(H*H.t())/N_non_missing;
if (alpha(2) != 0)
terr(i_e) += alpha(2)*accu(W)/N_non_missing;
if (beta(2) != 0)
terr(i_e) += beta(2)*accu(H)/N_non_missing;
}
/*
* This function calculates partition probability for
* a document.
*
* Ref: LDA production partition model by George Casella
*
*/
double TopicSearch::calc_ln_partition_probality(
vector<size_t> word_indices,
uvec Z) {
double partition_probability = 0.0;
mat beta_counts = zeros<mat> (this->num_topics_, this->vocabulary_size_);
// Calculate m_ji' s
for (size_t n = 0; n < word_indices.size(); n++)
beta_counts(Z(n), this->word_ids_(word_indices[n])) += 1;
// Calculate partition counts from m_ji' s; i' = 1 ... V
vec partition_counts = sum(beta_counts, 1); // sums over rows
// ln_gamma (n_j + alpha_j + 1)
vec ln_gamma_j = log_gamma_vec(partition_counts + this->alpha_vec_); // ln_gamma (n_j + alpha_j)
// ln a_j = \sum_i' (m_ji' * ln beta_ji')
vec ln_a_j = sum(beta_counts % this->ln_init_beta_sample_, 1); // sums over rows i.e. over i' s
partition_probability = accu(ln_gamma_j + ln_a_j); // sum over all j s - ln_gamma_K
return partition_probability;
}
/*!
* \brief convolutional layer forward
* X: [N, C, Hx, Wx]
* weight: [F, C, Hw, Ww]
* bias: [F, 1, 1, 1]
* out: [N, F, (Hx+pad*2-Hw)/stride+1, (Wx+pad*2-Ww)/stride+1]
* \param[in] const vector<Blob*>& in in[0]:X, in[1]:weights, in[2]:bias
* \param[in] const ConvParam* param conv params: stride, pad
* \param[out] Blob** out Y
*/
void ConvLayer::forward(const vector<shared_ptr<Blob>>& in,
shared_ptr<Blob>& out,
Param& param) {
if (out) {
out.reset();
}
assert(in[0]->get_C() == in[1]->get_C());
int N = in[0]->get_N();
int F = in[1]->get_N();
int C = in[0]->get_C();
int Hx = in[0]->get_H();
int Wx = in[0]->get_W();
int Hw = in[1]->get_H();
int Ww = in[1]->get_W();
// calc Hy, Wy
int Hy = (Hx + param.conv_pad*2 -Hw) / param.conv_stride + 1;
int Wy = (Wx + param.conv_pad*2 -Ww) / param.conv_stride + 1;
out.reset(new Blob(N, F, Hy, Wy));
Blob padX = (*in[0]).pad(param.conv_pad);
for (int n = 0; n < N; ++n) {
for (int f = 0; f < F; ++f) {
for (int hh = 0; hh < Hy; ++hh) {
for (int ww = 0; ww < Wy; ++ww) {
cube window = padX[n](span(hh * param.conv_stride, hh * param.conv_stride + Hw - 1),
span(ww * param.conv_stride, ww * param.conv_stride + Ww - 1),
span::all);
(*out)[n](hh, ww, f) = accu(window % (*in[1])[f]) + as_scalar((*in[2])[f]);
}
}
}
}
return;
}
//Calculation of BICreg
List Vect::bicReggen(vector<int> vectH, vector<int> vectY, int numr)
{
double reg = 0.0, sign, val;
// Ici, H est la matrice réponse.
mat H=Vect::const_matrix(vectH);
int n = H.n_rows,v = H.n_cols;
//construction of the matrix X
int a;
if (vectY.empty())
a=0;
else
a=vectY.size();
mat X(n,a+1);
if (vectY.empty())
X.col(0) = ones<colvec>(n);
else
{
mat Y = Vect::const_matrix(vectY);
Y.insert_cols(0, ones<colvec>(n));
X = Y;
}
//Parameter estimation
mat XtX = X.t() * X;
mat B = inv_sympd(XtX) * X.t() *H;
//mat B = pinv(XtX) * X.t() *H;
double lambda;
mat A=X*B;
if (numr==3) //(r=[LC])
{
mat Omega = (1.0/n)*(H.t()*(H-A));
Omega = 2*M_PI*Omega;
log_det(val, sign, Omega);
double det = log(sign*exp(val));
lambda = ((a+1)*v) + (0.5*v*(v+1));
reg = (-n*det)-(n*v)-(lambda*log(n));
}
if (numr==2) //(r=[LB])
{
mat H_A = (1.0/n)*(H - A)%(H - A);
rowvec sigma2 = sum(H_A, 0);
sigma2 = log(sigma2);
lambda=(v*(a+1)) +v;
reg=-(n*v*log(2*M_PI)) - (n* sum(sigma2)) -(n*v) - (lambda*log(n));
}
if (numr==1) //(r=[LI])
{
mat Aux=H-A;
double sigma=(1.0/(n*v))* accu(Aux % Aux);
lambda=(v*(a+1)) + 1;
reg=-(n*v*log(2*M_PI*sigma)) -(n*v) - (lambda*log(n));
}
return List::create(Named("bicvalue") = reg,
Named("B") = B);
}//end Vect::bicReggen