double RegularizedSVDFunction::Evaluate(const arma::mat& parameters) const
{
// The cost for the optimization is as follows:
// f(u, v) = sum((rating(i, j) - u(i).t() * v(j))^2)
// The sum is over all the ratings in the rating matrix.
// 'i' points to the user and 'j' points to the item being considered.
// The regularization term is added to the above cost, where the vectors u(i)
// and v(j) are regularized for each rating they contribute to.
double cost = 0.0;
for (size_t i = 0; i < data.n_cols; i++)
{
// Indices for accessing the the correct parameter columns.
const size_t user = data(0, i);
const size_t item = data(1, i) + numUsers;
// Calculate the squared error in the prediction.
const double rating = data(2, i);
double ratingError = rating - arma::dot(parameters.col(user),
parameters.col(item));
double ratingErrorSquared = ratingError * ratingError;
// Calculate the regularization penalty corresponding to the parameters.
double userVecNorm = arma::norm(parameters.col(user), 2);
double itemVecNorm = arma::norm(parameters.col(item), 2);
double regularizationError = lambda * (userVecNorm * userVecNorm +
itemVecNorm * itemVecNorm);
cost += (ratingErrorSquared + regularizationError);
}
return cost;
}
arma::mat Vespucci::Math::Transform::cwt_spdbc_mat(const arma::mat &X, std::string wavelet, arma::uword qscale,
double threshold, std::string threshold_method,
arma::uword window_size, arma::field<arma::umat> &peak_positions,
arma::mat &baselines)
{
baselines.set_size(X.n_rows, X.n_cols);
arma::vec baseline;
arma::vec spectrum;
arma::vec current_corrected;
arma::mat corrected(X.n_rows, X.n_cols);
arma::umat current_peakpos;
peak_positions.set_size(X.n_cols);
arma::uword i;
try{
for (i = 0; i < X.n_cols; ++i){
spectrum = X.col(i);
current_corrected = Vespucci::Math::Transform::cwt_spdbc(spectrum, wavelet,
qscale, threshold,
threshold_method, window_size,
current_peakpos, baseline);
peak_positions(i) = current_peakpos;
baselines.col(i) = baseline;
corrected.col(i) = current_corrected;
}
}catch(std::exception e){
std::cerr << std::endl << "exception! cwt_spdbc_mat" << std::endl;
std::cerr << "i = " << i << std::endl;
std::cerr << e.what();
throw(e);
}
return corrected;
}
void RegularizedSVDFunction<MatType>::Gradient(const arma::mat& parameters,
const size_t start,
GradType& gradient,
const size_t batchSize) const
{
gradient.zeros(rank, numUsers + numItems);
// It's possible this could be SIMD-vectorized for additional speedup.
for (size_t i = start; i < start + batchSize; ++i)
{
const size_t user = data(0, i);
const size_t item = data(1, i) + numUsers;
// Prediction error for the example.
const double rating = data(2, i);
double ratingError = rating - arma::dot(parameters.col(user),
parameters.col(item));
// Gradient is non-zero only for the parameter columns corresponding to the
// example.
gradient.col(user) += 2 * (lambda * parameters.col(user) -
ratingError * parameters.col(item));
gradient.col(item) += 2 * (lambda * parameters.col(item) -
ratingError * parameters.col(user));
}
}
/**
* Calculates and stores the gradient values given a set of parameters.
*/
void SoftmaxRegressionFunction::Gradient(const arma::mat& parameters,
arma::mat& gradient) const
{
// Calculate the class probabilities for each training example. The
// probabilities for each of the classes are given by:
// p_j = exp(theta_j' * x_i) / sum(exp(theta_k' * x_i))
// The sum is calculated over all the classes.
// x_i is the input vector for a particular training example.
// theta_j is the parameter vector associated with a particular class.
arma::mat probabilities;
GetProbabilitiesMatrix(parameters, probabilities);
// Calculate the parameter gradients.
gradient.set_size(parameters.n_rows, parameters.n_cols);
if (fitIntercept)
{
// Treating the intercept term parameters.col(0) seperately to avoid
// the cost of building matrix [1; data].
arma::mat inner = probabilities - groundTruth;
gradient.col(0) =
inner * arma::ones<arma::mat>(data.n_cols, 1) / data.n_cols +
lambda * parameters.col(0);
gradient.cols(1, parameters.n_cols - 1) =
inner * data.t() / data.n_cols +
lambda * parameters.cols(1, parameters.n_cols - 1);
}
else
{
gradient = (probabilities - groundTruth) * data.t() / data.n_cols +
lambda * parameters;
}
}
/**
* Construct a 2-class dataset out of noisy sines.
*
* @param data Input data used to store the noisy sines.
* @param labels Labels used to store the target class of the noisy sines.
* @param points Number of points/features in a single sequence.
* @param sequences Number of sequences for each class.
* @param noise The noise factor that influences the sines.
*/
void GenerateNoisySines(arma::mat& data,
arma::mat& labels,
const size_t points,
const size_t sequences,
const double noise = 0.3)
{
arma::colvec x = arma::linspace<arma::Col<double> >(0,
points - 1, points) / points * 20.0;
arma::colvec y1 = arma::sin(x + arma::as_scalar(arma::randu(1)) * 3.0);
arma::colvec y2 = arma::sin(x / 2.0 + arma::as_scalar(arma::randu(1)) * 3.0);
data = arma::zeros(points, sequences * 2);
labels = arma::zeros(2, sequences * 2);
for (size_t seq = 0; seq < sequences; seq++)
{
data.col(seq) = arma::randu(points) * noise + y1 +
arma::as_scalar(arma::randu(1) - 0.5) * noise;
labels(0, seq) = 1;
data.col(sequences + seq) = arma::randu(points) * noise + y2 +
arma::as_scalar(arma::randu(1) - 0.5) * noise;
labels(1, sequences + seq) = 1;
}
}
// [[Rcpp::export]]
arma::vec gradient_logPosterior_nogammas (double temp, arma::vec event, arma::uvec idGK_fast,
arma::vec event_colSumsW1, arma::mat W1s, arma::vec Bs_gammas,
arma::vec event_colSumsWlong, arma::mat Wlongs, arma::vec alphas,
arma::vec Pw,
arma::vec mean_Bs_gammas, arma::mat Tau_Bs_gammas,
arma::vec mean_alphas, arma::mat Tau_alphas,
double tauBs, double A_tauBs, double B_tauBs) {
vec Int = Pw % exp(W1s * Bs_gammas + Wlongs * alphas);
// gradient Bs_gammas
unsigned int n_Bs_gammas = Bs_gammas.n_rows;
vec score_Bs_gammas = vec(n_Bs_gammas, fill::zeros);
for (uword i = 0; i < n_Bs_gammas; ++i) {
vec H = W1s.col(i) % Int;
score_Bs_gammas[i] = temp * (event_colSumsW1[i] - sum(H));
}
score_Bs_gammas = score_Bs_gammas - tauBs * (Tau_Bs_gammas * (Bs_gammas - mean_Bs_gammas));
// gradient alphas
unsigned int n_alphas = alphas.n_rows;
vec score_alphas = vec(n_alphas, fill::zeros);
for (uword i = 0; i < n_alphas; ++i) {
vec H = Wlongs.col(i) % Int;
score_alphas[i] = temp * (event_colSumsWlong[i] - sum(H));
}
score_alphas = score_alphas - (Tau_alphas * (alphas - mean_alphas));
// gradient tauBs
vec z = Bs_gammas - mean_Bs_gammas;
vec score_tauBs = tauBs * (- 0.5 * (z.t() * Tau_Bs_gammas * z) + (A_tauBs - 1) / tauBs - B_tauBs);
// export results
vec out = join_cols(score_Bs_gammas, score_alphas);
out = join_cols(out, score_tauBs);
return(out);
}
// The step size should be chosen carefully to guarantee convergence given a
// reasonable number of computations.
int GradientDescent::RunGradientDescent(const Data &data) {
assert(num_iters_ >= 1);
const int kNumTrainEx = data.num_train_ex();
assert(kNumTrainEx >= 1);
const arma::mat kTrainingFeatures = data.training_features();
const arma::vec kTrainingLabels = data.training_labels();
double *j_theta_array = new double[num_iters_];
// Recall that we are trying to minimize the following cost function:
// ((training features) * (current weights) - (training labels))^2
// Each iteration of this algorithm updates the weights as a scaled
// version of the gradient of this cost function.
// This gradient is computed with respect to the weights.
// Thus, each iteration of gradient descent performs the following:
// (update) = (step size) * ((training features) * (current weights) - (training labels)) * (training features)
// (new weights) = (current weights) - (update)
for(int theta_index=0; theta_index<num_iters_; theta_index++)
{
const arma::vec kDiffVec = kTrainingFeatures*theta_-kTrainingLabels;
const arma::mat kDiffVecTimesTrainFeat = \
join_rows(kDiffVec % kTrainingFeatures.col(0),\
kDiffVec % kTrainingFeatures.col(1));
const arma::vec kThetaNew = theta_-alpha_*(1/(float)kNumTrainEx)*\
(sum(kDiffVecTimesTrainFeat)).t();
j_theta_array[theta_index] = ComputeCost(data);
set_theta(kThetaNew);
}
delete [] j_theta_array;
return 0;
}
void
HMM::cacheProbabilities(const arma::mat & data) {
for (unsigned int i = 0; i < N_; ++i) {
arma::vec weights = BModels_[i].getWeights();
for (unsigned int l = 0; l < weights.n_elem; ++l) {
const GM & gm = BModels_[i].getGM(l);
gammaLts_[i].col(l) = weights(l) * arma::trans(gm.getDataProb(data));
}
B_.col(i) = arma::sum(gammaLts_[i],1);
}
if (!B_.is_finite()) {
//B_.print("B");
for (unsigned int i = 0; i < N_; ++i) {
arma::vec test = B_.col(i);
if (!test.is_finite()) {
arma::vec weights = BModels_[i].getWeights();
for (unsigned l = 0; l < weights.n_elem; ++l) {
arma::vec test2 = gammaLts_[i].col(l);
if (!test2.is_finite()) {
const GM & gm = BModels_[i].getGM(l);
gm.print("gm");
arma::vec test3 = arma::trans(gm.getDataProb(data));
//test3.print("test3");
}
}
}
}
throw std::runtime_error("probabilities not finite");
}
}
void LovaszThetaSDP::GradientConstraint(const size_t index,
const arma::mat& coordinates,
arma::mat& gradient)
{
// Log::Debug << "Gradient of constraint " << index << " is " << std::endl;
if (index == 0) // This is the constraint Tr(X) = 1.
{
gradient = 2 * coordinates; // d/dR (Tr(R R^T)) = 2 R.
// std::cout << gradient;
return;
}
// Log::Debug << "Evaluating gradient of constraint " << index << " with ";
size_t i = edges(0, index - 1);
size_t j = edges(1, index - 1);
// Log::Debug << "i = " << i << " and j = " << j << "." << std::endl;
// Since the constraint is (R^T R)_ij, the gradient for (x, y) will be (I
// derived this for one of the MVU constraints):
// 0 , y != i, y != j
// 2 R_xj, y = i, y != j
// 2 R_xi, y != i, y = j
// 4 R_xy, y = i, y = j
// This results in the gradient matrix having two nonzero rows; for row
// i, the elements are R_nj, where n is the row; for column j, the elements
// are R_ni.
gradient.zeros(coordinates.n_rows, coordinates.n_cols);
gradient.col(i) = coordinates.col(j);
gradient.col(j) += coordinates.col(i); // In case j = i (shouldn't happen).
// std::cout << gradient;
}
void FFN<
LayerTypes, OutputLayerType, InitializationRuleType, PerformanceFunction
>::Predict(arma::mat& predictors, arma::mat& responses)
{
deterministic = true;
arma::mat responsesTemp;
ResetParameter(network);
Forward(arma::mat(predictors.colptr(0), predictors.n_rows, 1, false, true),
network);
OutputPrediction(responsesTemp, network);
responses = arma::mat(responsesTemp.n_elem, predictors.n_cols);
responses.col(0) = responsesTemp.col(0);
for (size_t i = 1; i < predictors.n_cols; i++)
{
Forward(arma::mat(predictors.colptr(i), predictors.n_rows, 1, false, true),
network);
responsesTemp = arma::mat(responses.colptr(i), responses.n_rows, 1, false,
true);
OutputPrediction(responsesTemp, network);
responses.col(i) = responsesTemp.col(0);
}
}
/**
* The update rule for the encoding matrix H.
* The function takes in all the matrices and only changes the
* value of the H matrix.
*
* @param V Input matrix to be factorized.
* @param W Basis matrix.
* @param H Encoding matrix to be updated.
*/
inline void HUpdate(const MatType& V,
const arma::mat& W,
arma::mat& H)
{
arma::mat deltaH;
deltaH.zeros(H.n_rows, 1);
const double val = V(currentItemIndex, currentUserIndex);
// Update H matrix based on the non-zero entry found in WUpdate function.
deltaH += (val - arma::dot(W.row(currentItemIndex),
H.col(currentUserIndex))) * W.row(currentItemIndex).t();
// Add regularization.
if (kh != 0)
deltaH -= kh * H.col(currentUserIndex);
// Move on to the next entry.
currentUserIndex = currentUserIndex + 1;
if (currentUserIndex == V.n_rows)
{
currentUserIndex = 0;
currentItemIndex = (currentItemIndex + 1) % V.n_cols;
}
H.col(currentUserIndex++) += u * deltaH;
}
// Fits an alpha and beta parameter according to observation probabilities.
void GammaDistribution::Train(const arma::mat& rdata,
const arma::vec& probabilities,
const double tol)
{
// If fittingSet is empty, nothing to do.
if (arma::size(rdata) == arma::size(arma::mat()))
return;
arma::vec meanLogxVec(rdata.n_rows, arma::fill::zeros);
arma::vec meanxVec(rdata.n_rows, arma::fill::zeros);
arma::vec logMeanxVec(rdata.n_rows, arma::fill::zeros);
for (size_t i = 0; i < rdata.n_cols; i++)
{
meanLogxVec += probabilities(i) * arma::log(rdata.col(i));
meanxVec += probabilities(i) * rdata.col(i);
}
double totProbability = arma::accu(probabilities);
meanLogxVec /= totProbability;
meanxVec /= totProbability;
logMeanxVec = arma::log(meanxVec);
// Call the statistics-only GammaDistribution::Train() function to fit the
// parameters. That function does all the work so we're done.
Train(logMeanxVec, meanLogxVec, meanxVec, tol);
}
/**
* The update rule for the basis matrix W.
* The function takes in all the matrices and only changes the
* value of the W matrix.
*
* @param V Input matrix to be factorized.
* @param W Basis matrix to be updated.
* @param H Encoding matrix.
*/
inline void WUpdate(const arma::sp_mat& V,
arma::mat& W,
const arma::mat& H)
{
if(!isStart) (*it)++;
else isStart = false;
if(*it == V.end())
{
delete it;
it = new arma::sp_mat::const_iterator(V.begin());
}
size_t currentUserIndex = it->col();
size_t currentItemIndex = it->row();
arma::mat deltaW(1, W.n_cols);
deltaW.zeros();
deltaW += (**it - arma::dot(W.row(currentItemIndex), H.col(currentUserIndex)))
* arma::trans(H.col(currentUserIndex));
if(kw != 0) deltaW -= kw * W.row(currentItemIndex);
W.row(currentItemIndex) += u*deltaW;
}
/**
* Estimate the Gaussian distribution from the given observations, taking into
* account the probability of each observation actually being from this
* distribution.
*/
void GaussianDistribution::Estimate(const arma::mat& observations,
const arma::vec& probabilities)
{
if (observations.n_cols > 0)
{
mean.zeros(observations.n_rows);
covariance.zeros(observations.n_rows, observations.n_rows);
}
else // This will end up just being empty.
{
mean.zeros(0);
covariance.zeros(0);
return;
}
double sumProb = 0;
// First calculate the mean, and save the sum of all the probabilities for
// later normalization.
for (size_t i = 0; i < observations.n_cols; i++)
{
mean += probabilities[i] * observations.col(i);
sumProb += probabilities[i];
}
if (sumProb == 0)
{
// Nothing in this Gaussian! At least set the covariance so that it's
// invertible.
covariance.diag() += 1e-50;
return;
}
// Normalize.
mean /= sumProb;
// Now find the covariance.
for (size_t i = 0; i < observations.n_cols; i++)
{
arma::vec obsNoMean = observations.col(i) - mean;
covariance += probabilities[i] * (obsNoMean * trans(obsNoMean));
}
// This is probably biased, but I don't know how to unbias it.
covariance /= sumProb;
// Ensure that the covariance is positive definite.
if (det(covariance) <= 1e-50)
{
Log::Debug << "GaussianDistribution::Estimate(): Covariance matrix is not "
<< "positive definite. Adding perturbation." << std::endl;
double perturbation = 1e-30;
while (det(covariance) <= 1e-50)
{
covariance.diag() += perturbation;
perturbation *= 10; // Slow, but we don't want to add too much.
}
}
}
/**
* The update rule for the basis matrix W. The function takes in all the
* matrices and only changes the value of the W matrix.
*
* @param V Input matrix to be factorized.
* @param W Basis matrix to be updated.
* @param H Encoding matrix.
*/
inline void WUpdate(const MatType& V,
arma::mat& W,
const arma::mat& H)
{
arma::mat deltaW;
deltaW.zeros(1, W.n_cols);
// Loop until a non-zero entry is found.
while(true)
{
const double val = V(currentItemIndex, currentUserIndex);
// Update feature vector if current entry is non-zero and break the loop.
if (val != 0)
{
deltaW += (val - arma::dot(W.row(currentItemIndex),
H.col(currentUserIndex))) * H.col(currentUserIndex).t();
// Add regularization.
if (kw != 0)
deltaW -= kw * W.row(currentItemIndex);
break;
}
}
W.row(currentItemIndex) += u * deltaW;
}
// [[Rcpp::depends(BH)]]
// [[Rcpp::depends(RcppArmadillo)]]
arma::mat intervals(arma::mat& means, const arma::mat& sds, const arma::vec& probs, unsigned int n_ahead) {
boost::math::tools::eps_tolerance<double> tol;
arma::mat intv(n_ahead, probs.n_elem);
for (unsigned int i = 0; i < n_ahead; i++) {
double lower = means.col(i).min() - 2 * sds.col(i).max();
double upper = means.col(i).max() + 2 * sds.col(i).max();
for (unsigned int j = 0; j < probs.n_elem; j++) {
boost::uintmax_t max_iter = 1000;
objective_gaussian f(means.col(i), sds.col(i), probs(j));
std::pair<double, double> r =
boost::math::tools::bisect(f, lower, upper, tol, max_iter);
if (!tol(r.first, r.second) || (max_iter >= 1000)) {
max_iter = 10000;
r = boost::math::tools::bisect(f, 1000 * lower, 1000 * upper, tol, max_iter);
}
intv(i, j) = r.first + (r.second - r.first) / 2.0;
lower = intv(i, j);
}
}
return intv;
}
arma::mat Vespucci::Math::Transform::cwtPeakAnalysis(const arma::mat &X,
std::string wavelet, arma::uword qscale,
double threshold, std::string threshold_method,
arma::mat &transform)
{
transform.set_size(X.n_rows, X.n_cols);
arma::uvec scales(1);
scales(0) = qscale;
arma::uword i;
arma::umat peak_positions;
arma::mat peak_extrema(X.n_rows, X.n_cols);
arma::vec spectrum, current_transform, dtransform, peak_magnitudes;
try{
for (i = 0; i < X.n_cols; ++i){
spectrum = X.col(i);
current_transform = Vespucci::Math::Transform::cwt(spectrum, wavelet, scales);
transform.col(i) = current_transform;
dtransform = Vespucci::Math::diff(transform, 1);
dtransform.insert_rows(0, 1, true); //dtransform(i) is derivative at transform(i)
peak_positions = Vespucci::Math::PeakFinding::FindPeakPositions(transform, dtransform,
threshold, threshold_method,
peak_magnitudes);
peak_extrema.col(i) = Vespucci::Math::PeakFinding::PeakExtrema(X.n_elem, peak_positions);
}
}
catch(std::exception e){
std::cerr << "CWTPeakAnalysis" << std::endl;
std::cerr << "i = " << i << std::endl;
throw(e);
}
return peak_extrema;
}
size_t MaxVarianceNewCluster::EmptyCluster(const MatType& data,
const size_t emptyCluster,
const arma::mat& oldCentroids,
arma::mat& newCentroids,
arma::Col<size_t>& clusterCounts,
MetricType& metric,
const size_t iteration)
{
// If necessary, calculate the variances and assignments.
if (iteration != this->iteration || assignments.n_elem != data.n_cols)
Precalculate(data, oldCentroids, clusterCounts, metric);
this->iteration = iteration;
// Now find the cluster with maximum variance.
arma::uword maxVarCluster;
variances.max(maxVarCluster);
// Now, inside this cluster, find the point which is furthest away.
size_t furthestPoint = data.n_cols;
double maxDistance = -DBL_MAX;
for (size_t i = 0; i < data.n_cols; ++i)
{
if (assignments[i] == maxVarCluster)
{
const double distance = std::pow(metric.Evaluate(data.col(i),
newCentroids.col(maxVarCluster)), 2.0);
if (distance > maxDistance)
{
maxDistance = distance;
furthestPoint = i;
}
}
}
// Take that point and add it to the empty cluster.
newCentroids.col(maxVarCluster) *= (double(clusterCounts[maxVarCluster]) /
double(clusterCounts[maxVarCluster] - 1));
newCentroids.col(maxVarCluster) -= (1.0 / (clusterCounts[maxVarCluster] - 1.0)) *
arma::vec(data.col(furthestPoint));
clusterCounts[maxVarCluster]--;
clusterCounts[emptyCluster]++;
newCentroids.col(emptyCluster) = arma::vec(data.col(furthestPoint));
assignments[furthestPoint] = emptyCluster;
// Modify the variances, as necessary.
variances[emptyCluster] = 0;
// One has already been subtracted from clusterCounts[maxVarCluster].
variances[maxVarCluster] = (1.0 / (clusterCounts[maxVarCluster])) *
((clusterCounts[maxVarCluster] + 1) * variances[maxVarCluster] - maxDistance);
// Output some debugging information.
Log::Debug << "Point " << furthestPoint << " assigned to empty cluster " <<
emptyCluster << ".\n";
return 1; // We only changed one point.
}
void NeuralNetwork::normalizeFeatures(arma::mat& input) const
{
//this needs to be tweaked. not okay..
for (unsigned int feature = 0; feature < input.n_cols; ++feature)
{
double mean = arma::mean(input.col(feature));
double stddev = arma::stddev(input.col(feature));
input.col(feature) = (input.col(feature) - mean) / stddev;
}
}
/**
* Estimate the Gaussian distribution from the given observations, taking into
* account the probability of each observation actually being from this
* distribution.
*/
void GaussianDistribution::Train(const arma::mat& observations,
const arma::vec& probabilities)
{
if (observations.n_cols > 0)
{
mean.zeros(observations.n_rows);
covariance.zeros(observations.n_rows, observations.n_rows);
}
else // This will end up just being empty.
{
// TODO(stephentu): same as above
mean.zeros(0);
covariance.zeros(0);
return;
}
double sumProb = 0;
// First calculate the mean, and save the sum of all the probabilities for
// later normalization.
for (size_t i = 0; i < observations.n_cols; i++)
{
mean += probabilities[i] * observations.col(i);
sumProb += probabilities[i];
}
if (sumProb == 0)
{
// Nothing in this Gaussian! At least set the covariance so that it's
// invertible.
covariance.diag() += 1e-50;
FactorCovariance();
return;
}
// Normalize.
if (sumProb > 0)
mean /= sumProb;
// Now find the covariance.
for (size_t i = 0; i < observations.n_cols; i++)
{
arma::vec obsNoMean = observations.col(i) - mean;
covariance += probabilities[i] * (obsNoMean * trans(obsNoMean));
}
// This is probably biased, but I don't know how to unbias it.
if (sumProb > 0)
covariance /= sumProb;
// Ensure that the covariance is positive definite.
gmm::PositiveDefiniteConstraint::ApplyConstraint(covariance);
FactorCovariance();
}
/**
* Initialize the dictionary randomly from a normal distribution, such that
* each atom has a norm of 1. This is simple enough to be included with the
* definition.
*
* @param data Dataset to use for initialization.
* @param atoms Number of atoms (columns) in the dictionary.
* @param dictionary Dictionary to initialize.
*/
static void Initialize(const arma::mat& data,
const size_t atoms,
arma::mat& dictionary)
{
// Create random dictionary.
dictionary.randn(data.n_rows, atoms);
// Normalize each atom.
for (size_t j = 0; j < atoms; ++j)
dictionary.col(j) /= norm(dictionary.col(j), 2);
}
void UpdateWeights(const VecType& trainingPoint,
arma::mat& weights,
arma::vec& biases,
const size_t incorrectClass,
const size_t correctClass,
const double instanceWeight = 1.0)
{
weights.col(incorrectClass) -= instanceWeight * trainingPoint;
biases(incorrectClass) -= instanceWeight;
weights.col(correctClass) += instanceWeight * trainingPoint;
biases(correctClass) += instanceWeight;
}
static inline force_inline size_t EmptyCluster(
const MatType& /* data */,
const size_t emptyCluster,
const arma::mat& oldCentroids,
arma::mat& newCentroids,
arma::Col<size_t>& /* clusterCounts */,
MetricType& /* metric */,
const size_t /* iteration */)
{
// Take the last iteration's centroid.
newCentroids.col(emptyCluster) = oldCentroids.col(emptyCluster);
return 0; // No points were changed.
}
/**
* This function is called to update the weightVectors matrix.
* It decreases the weights of the incorrectly classified class while
* increasing the weight of the correct class it should have been classified to.
*
* @param trainData The training dataset.
* @param weightVectors Matrix of weight vectors.
* @param rowIndex Index of the row which has been incorrectly predicted.
* @param labelIndex Index of the vector in trainData.
* @param vectorIndex Index of the class which should have been predicted.
* @param D Cost of mispredicting the labelIndex instance.
*/
void UpdateWeights(const arma::mat& trainData,
arma::mat& weightVectors,
const size_t labelIndex,
const size_t vectorIndex,
const size_t rowIndex,
const arma::rowvec& D)
{
weightVectors.row(rowIndex) = weightVectors.row(rowIndex) -
D(labelIndex) * trainData.col(labelIndex).t();
weightVectors.row(vectorIndex) = weightVectors.row(vectorIndex) +
D(labelIndex) * trainData.col(labelIndex).t();
}
void grow(statelist &state, parmlist &parms, arma::mat &R, uword j, uword s, int i) {
state.S(j) += 1;
state.B(j) = beta_f(parms.beta(state.S(j)), i, parms.max_inf(state.S(j)));
state.F += kernel2(distance(state, j), parms.m(state.S(j))) * i * (parms.lamda(state.S(j)) - parms.lamda(s));
state.E = fmax(0, 1 - sum(parms.omega(state.S)) / parms.K);
R.col(0) = state.E * parms.f(state.S);
R(j, 1) = parms.d(state.S(j)) + i * parms.alpha(state.S(j)) * (1 - parms.r(state.S(j)));
R(j, 2) = parms.g(state.S(j));
R.col(3) = (state.F + lamda_interp(state, parms)) % state.B;
R(j, 4) = i * parms.mu(state.S(j));
R(j, 5) = i * parms.alpha(state.S(j)) * parms.r(state.S(j));
}
arma::mat ss::dsim(double Ts, arma::mat const &u){
setsizes();
mat ysim(ny, u.n_cols);
mat xsim;
xsim = zeros(nx, 1);
ysim.col(0) = C * xsim;
for (uword i = 1; i < u.n_cols; i++){ /*simple euler*/
//xsim = xsim + Ts*(A*xsim + B*u.col(i));
xsim = (A*xsim + B*u.col(i));
ysim.col(i) = C * xsim + D * u.col(i);
}
return ysim;
}
//[[Rcpp::export]]
List GibbsRegress (arma::mat y, arma::mat x, int N=1000, int burnin=500){
int n = y.n_cols;
arma::mat beta(3,1); beta.fill(0);
double sigma2 =1;
arma::mat sbeta(N-burnin,3); //
arma::colvec ssigma2(N-burnin); //
/* valores para os hiperparâmetros da a priori */
double a=2.1, b=1.1, m_0=0, m_1=0, m_2=0, v_0=10, v_1=10, v_2=10;
for(int t=0; t<N; t++){
arma::mat mi = x*beta ;
double soma = arma::as_scalar( sum( pow( y-mi, 2) ) );
double A = a + 0.5*n;
double B = b + 0.5*soma;
sigma2 = 1/R::rgamma(A,1/B); // gerando sigma2
//printf("sigma2:%f \n",sigma2);
double rest0 = 0, soma1=0;
for(int i=0; i<n; i++){
rest0 = arma::as_scalar( x.row(i)*beta - beta(0,0)*x(i,0) );
soma1 += ( y(i,0)-rest0);
}
double V0= 1/( (n/sigma2)+(1/v_0) );
double M0= V0*( (soma1/sigma2) + (m_0/v_0));
beta(0,0)=R::rnorm(M0,sqrt(V0)); // gerando b0
double rest1=0, soma2=0;
for(int i=0; i<n; i++){
rest1 = arma::as_scalar( x.row(i)*beta - beta(1,0)*x(i,1) );
soma2 += x(i,1)*( y(i,0)-rest1);
}
double V1=1/( arma::as_scalar( (sum( pow(x.col(1),2) ))/sigma2 ) + (1/v_1));
double M1=V1*( (soma2/sigma2) + (m_1/v_1) );
beta(1,0)=R::rnorm(M1,sqrt(V1));
double rest2=0, soma3=0;
for(int i=0; i<n; i++){
rest2 = arma::as_scalar( x.row(i)*beta - beta(2,0)*x(i,2) );
soma3 += x(i,2)*( y(i,0)-rest2);
}
double V2=1/( arma::as_scalar( (sum( pow(x.col(2),2 ) ))/sigma2) +(1/v_2) );
double M2=V2*((soma3/sigma2) + (m_2/v_2) );
beta(2,0)=R::rnorm(M2,sqrt(V2));
if(t>burnin){
sbeta.row(t-burnin)=beta.t();
ssigma2(t-burnin)=sigma2; }
}
List saida;
saida["betas"]=sbeta;
saida["sigma2"]=ssigma2;
return saida;
}
/***
* Calculate the gradient.
*/
void RosenbrockWoodFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
gradient.set_size(4, 2);
arma::vec grf(4);
arma::vec gwf(4);
rf.Gradient(coordinates.col(0), grf);
wf.Gradient(coordinates.col(1), gwf);
gradient.col(0) = grf;
gradient.col(1) = gwf;
}
/**
* Estimate the Gaussian distribution directly from the given observations.
*
* @param observations List of observations.
*/
void GaussianDistribution::Train(const arma::mat& observations)
{
if (observations.n_cols > 0)
{
mean.zeros(observations.n_rows);
covariance.zeros(observations.n_rows, observations.n_rows);
}
else // This will end up just being empty.
{
// TODO(stephentu): why do we allow this case? why not throw an error?
mean.zeros(0);
covariance.zeros(0);
return;
}
// Calculate the mean.
for (size_t i = 0; i < observations.n_cols; i++)
mean += observations.col(i);
// Normalize the mean.
mean /= observations.n_cols;
// Now calculate the covariance.
for (size_t i = 0; i < observations.n_cols; i++)
{
arma::vec obsNoMean = observations.col(i) - mean;
covariance += obsNoMean * trans(obsNoMean);
}
// Finish estimating the covariance by normalizing, with the (1 / (n - 1)) so
// that it is the unbiased estimator.
covariance /= (observations.n_cols - 1);
// Ensure that the covariance is positive definite.
if (det(covariance) <= 1e-50)
{
Log::Debug << "GaussianDistribution::Train(): Covariance matrix is not "
<< "positive definite. Adding perturbation." << std::endl;
double perturbation = 1e-30;
while (det(covariance) <= 1e-50)
{
covariance.diag() += perturbation;
perturbation *= 10; // Slow, but we don't want to add too much.
}
}
FactorCovariance();
}
/**
* This function is called to update the weightVectors matrix. It decreases
* the weights of the incorrectly classified class while increasing the weight
* of the correct class it should have been classified to.
*
* @param trainData The training dataset.
* @param weightVectors Matrix of weight vectors.
* @param rowIndex Index of the row which has been incorrectly predicted.
* @param labelIndex Index of the vector in trainData.
* @param vectorIndex Index of the class which should have been predicted.
* @param D Cost of mispredicting the labelIndex instance.
*/
void UpdateWeights(const arma::mat& trainData,
arma::mat& weightVectors,
const size_t labelIndex,
const size_t vectorIndex,
const size_t rowIndex,
const arma::rowvec& D)
{
weightVectors.row(rowIndex).subvec(1, weightVectors.n_cols - 1) -=
D(labelIndex) * trainData.col(labelIndex).t();
weightVectors(rowIndex, 0) -= D(labelIndex);
weightVectors.row(vectorIndex).subvec(1, weightVectors.n_cols - 1) +=
D(labelIndex) * trainData.col(labelIndex).t();
weightVectors(vectorIndex, 0) += D(labelIndex);
}