void CosineTreeBuilder::CTNode(arma::mat A, CosineTree& root)
{
A = A.t();
Log::Info<<"CTNode"<<std::endl;
//Calculating Centroid
arma::rowvec centroid = CalculateCentroid(A);
//Calculating sampling probabilities
arma::vec probabilities = arma::zeros<arma::vec>(A.n_rows,1);
LSSampling(A,probabilities);
//Setting Values
root.Probabilities(probabilities);
root.Data(A);
root.Centroid(centroid);
}
// [[Rcpp::export]]
arma::vec innerLoop(arma::vec resp,
arma::vec beta, double intercept,
double tol, int max_iter,
arma::mat x_mat,
int n, arma::vec weights) {
bool converge = false;
int counter = 0;
arma::vec temp_resp;
arma::vec beta_new = beta;
double intercept_new;
while(!converge && counter < max_iter) {
temp_resp = x_mat.t() * ((resp - intercept) / n);
// The argmin is hence equivalent to that of
// (1/2) * ||v - beta||_2^2 + 4 * lam * Pen(beta).
// In main func weights will be weights.col(i)
beta_new = GetProxOne(temp_resp, 4 * weights);
intercept_new = mean(resp - x_mat * beta_new);
double change1 = pow(intercept_new - intercept, 2) + sum(square(beta_new - beta));
double change2 = pow(intercept_new, 2) + sum(square(beta_new));;
if( pow(change1, 0.5) / pow(change2, 0.5) < tol ) {
beta = beta_new;
intercept = intercept_new;
converge = true;
} else {
beta = beta_new;
intercept = intercept_new;
counter = counter + 1;
if(counter == max_iter) {
beta = beta_new;
intercept = intercept_new;
Function warning("warning");
warning("Function did not converge for inner loop for some lambda.");
}
}
}
arma::vec inter_vec(1);
inter_vec(0) = intercept;
return join_vert(inter_vec, beta);
}
// [[Rcpp::export]]
arma::mat expskewC(arma::mat M){
/*This function takes a 3-by-3 skew symmetric matrix (in so(3)) and
returns the exponential, a 3-by-3 rotations (in SO(3))*/
double MMt = sum(sum(M-M.t()));
if(fabs(MMt)>0.01){
throw Rcpp::exception("The exp.skew function is expecting a 3-by-3 skew symmetric matrix");
}
arma::mat expM(3,3);
expM.eye();
double a = pow(0.5*trace(M.t()*M),0.5);
if(a < 0.000001 && a > -0.000001){
return expM;
}
expM = expM + (sin(a)/a) * M + (1-cos(a))*pow(a,-2)*M*M;
return expM;
}
//evaluate Hessian operator on Z
//eucH is the ordinary Hessian matrix on Z in the ambient space
//return <Z, Hessian*Z>_Y
double specialLinear::evalHessian(const arma::mat & eucH,const arma::mat & Z){
arma::mat YU,eucH_proj,Weingarten,Weingarten_part,temp;
//project euclidian Hessian onto tangent space
YU=eucH*Y.i();
YU=1.0/n*(arma::trace(YU))*Y;
eucH_proj=eucH-YU;
//Weingarten Map
Weingarten=-1.0/n*(arma::dot(eucH.t(),Y.i()))*Z;
Weingarten_part=1.0/n*eucH*Y.i()*Z;
temp=1.0/n*(arma::dot(Weingarten_part.t(),Y.i()))*Y;
Weingarten_part-=temp;
Weingarten+=Weingarten_part;
hessian_Z=eucH_proj+Weingarten;
Z_hessian_Z=arma::dot(hessian_Z,Z);
return Z_hessian_Z;
}
arma::vec cpp_UpdateGamma (arma::mat x_big, arma::vec weights_big,
arma::vec y_big,
arma::vec gamma, arma::vec beta,
double lambda) {
// Another helper function used by the main algorithm.
// In this algorithm we loop through and do a coordinate wise update of
// gamma.
//
// Agrs:
// beta/gamma: The 'current' parameter vectors.
// x/weights/y_big: Design, weights and response for the big population.
// lambda: The value of the penalty parameter.
// Returns:
// gamma: The updated gamma vector.
// Obtain value of dimension.
int p = gamma.size();
// Initialize matrix X * beta.
arma::mat x_beta = x_big * beta;
// We need the diagonal entries of X^T * W * X.
// This is easy when W is a diagonal matrix.
arma::mat W_times_X(x_big.begin(), x_big.n_rows, x_big.n_cols, true);
W_times_X.each_col() %= weights_big;
// We obtain the diagonal entries of X^T * W * X for the denominators.
arma::mat Xt_W_X = x_big.t() * W_times_X;
arma::vec denoms = Xt_W_X.diag();
// Some temporary vectors which we use later.
arma::vec temp_gamma(gamma.begin(), gamma.size(), true);
double temp1;
// Loop through the different gamma values which need to be updated.
for(int i = 0; i < p; i++) {
// Instead of excluding a column we simply set gamma_j = 0 to get the fitted
// value without the effect of gamma_j.
temp_gamma(i) = 0;
temp1 = as_scalar(x_big.col(i).t() * (weights_big % (y_big - x_beta - x_big * temp_gamma)));
gamma(i) = (cpp_sign(temp1) * cpp_max(abs(temp1) - lambda, 0.0))/denoms(i);
temp_gamma(i) = gamma(i);
}
return gamma;
}
// [[Rcpp::export]]
arma::mat logSO3C(arma::mat R){
arma::mat I(3,3), logR(3,3);
I.eye();
double theta = acos(0.5*trace(R)-0.5);
if(theta < 0.0001){
logR.zeros();
return logR;
}
logR = (R-R.t())*theta/(2*sin(theta));
return logR;
}
// Uses singular value decomposition function svd() from Armadillo.
// Thus, be sure to define the following in /path/to/armadillo/include/armadillo_bits/config.hpp:
// ARMA_USE_LAPACK
// ARMA_USE_BLAS
// ARMA_BLAS_UNDERSCORE
int PCA::Run(const DataUnlabeledNormalized &data_unlabeled_normalized) {
const int kNumTrainEx = data_unlabeled_normalized.num_train_ex();
assert(kNumTrainEx >= 1);
const arma::mat kTrainingFeatures = \
data_unlabeled_normalized.training_features_normalized();
const arma::mat kCovMat = \
(1.0/(float)kNumTrainEx)*kTrainingFeatures.t()*kTrainingFeatures;
const int kNumRows = kCovMat.n_rows;
arma::mat left_sing_vec = arma::zeros<arma::mat>(kNumRows,kNumRows);
arma::vec sing_val = arma::zeros<arma::vec>(kNumRows,1);
arma::mat right_sing_vec = arma::zeros<arma::mat>(kNumRows,kNumRows);
arma::svd(left_sing_vec,sing_val,right_sing_vec,kCovMat);
this->set_left_sing_vec(left_sing_vec);
this->set_sing_val(sing_val);
return 0;
}
// // [[Rcpp::export()]]
arma::mat getEx2x2_ordIRT(const arma::mat &Ex,
const arma::mat &Vx,
const int N) {
arma::mat Ex2x2(2, 2, arma::fill::zeros) ;
arma::mat tmp(1, 1) ;
tmp.fill(N) ;
arma::mat S = tmp % Vx + Ex.t() * Ex ;
Ex2x2(0, 0) = N ;
Ex2x2(1, 1) = S(0,0) ;
arma::mat sums = sum(Ex, 0) ;
Ex2x2(1, 0) = sums(0,0) ;
Ex2x2(0, 1) = sums(0,0) ;
return(Ex2x2) ;
}
double
HMM::forwardProcedureCached() {
//initialisation
alpha_.col(0) = arma::trans(pi_ % B_.row(0));
c_(0) = arma::accu(alpha_.col(0));
alpha_.col(0) /= arma::as_scalar(c_(0));
//alpha_.print("alpha");
//c_.print("scale");
//iteration
for(unsigned int t = 1; t < T_; ++t) {
alpha_.col(t) = (A_.t() * alpha_.col(t-1)) % arma::trans(B_.row(t));
c_(t) = arma::accu(alpha_.col(t));
alpha_.col(t) /= arma::as_scalar(c_(t));
}
pprob_ = arma::accu(arma::log(c_));
return pprob_;
}
// [[Rcpp::export]]
arma::rowvec meanQ4C(arma::mat Q) {
//Compute the projected mean of the sample Q
NumericMatrix Qss = as<NumericMatrix>(wrap(Q));
int cq4 = checkQ4(Qss);
if(cq4){
throw Rcpp::exception("The data are not in Q4.");
}
arma::mat Qsq=Q.t()*Q;
arma::mat eigvec;
arma::vec eigval;
arma::eig_sym(eigval,eigvec,Qsq);
arma::vec qhat=eigvec.col(3);
if(qhat[0]<0){
qhat = -qhat;
}
return qhat.t(); //Want to return it in a row vector so transpose it
}
/**
* Compute
*
* alpha = min(1, tau * alphahat(A, dA))
*
* where
*
* alphahat = sup{ alphahat : A + dA is psd }
*
* See (2.18) of [AHO98] for more details.
*/
static inline double
Alpha(const arma::mat& A, const arma::mat& dA, double tau)
{
// On Armadillo < 4.500, the "lower" option isn't available.
#if (ARMA_VERSION_MAJOR < 4) || \
((ARMA_VERSION_MAJOR == 4) && (ARMA_VERSION_MINOR < 500))
const arma::mat L = arma::chol(A).t(); // This is less efficient.
#else
const arma::mat L = arma::chol(A, "lower");
#endif
const arma::mat Linv = arma::inv(arma::trimatl(L));
// TODO(stephentu): We only want the top eigenvalue, we should
// be able to do better than full eigen-decomposition.
const arma::vec evals = arma::eig_sym(-Linv * dA * Linv.t());
const double alphahatinv = evals(evals.n_elem - 1);
double alphahat = 1. / alphahatinv;
if (alphahat < 0.)
// dA is PSD already
alphahat = 1.;
return std::min(1., tau * alphahat);
}
// [[Rcpp::export]]
arma::rowvec HnCpp(arma::mat Qs){
//Compute the Hn tests statistics
int n = Qs.n_rows, i=0;
arma::mat T = Qs.t()*Qs;
arma::mat eigvec, eigvecJ;
arma::vec eigval, eigvalJ;
arma::eig_sym(eigval,eigvec,T);
arma::rowvec Hn(n);
arma::rowvec Qj;
arma::mat Tj;
for(i = 0;i<n; i++){
Qj = Qs.row(i);
Tj = T-Qj.t()*Qj;
arma::eig_sym(eigvalJ,eigvecJ,Tj);
Hn(i)=(n-2)*(1+eigvalJ(3)-eigval(3))/(n-1-eigvalJ(3));
}
return Hn;
}
NumericVector logLikMixHMM(const arma::mat& transition, const arma::cube& emission,
const arma::vec& init, const arma::ucube& obs, const arma::mat& coef, const arma::mat& X,
const arma::uvec& numberOfStates, unsigned int threads) {
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
return wrap(-arma::datum::inf);
}
weights.each_row() /= sum(weights, 0);
arma::vec ll(obs.n_slices);
arma::sp_mat transition_t(transition.t());
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) num_threads(threads) \
default(none) shared(ll, obs, weights, init, emission, transition_t, numberOfStates)
for (unsigned int k = 0; k < obs.n_slices; k++) {
arma::vec alpha = init % reparma(weights.col(k), numberOfStates);
for (unsigned int r = 0; r < obs.n_rows; r++) {
alpha %= emission.slice(r).col(obs(r, 0, k));
}
double tmp = sum(alpha);
ll(k) = log(tmp);
alpha /= tmp;
for (unsigned int t = 1; t < obs.n_cols; t++) {
alpha = transition_t * alpha;
for (unsigned int r = 0; r < obs.n_rows; r++) {
alpha %= emission.slice(r).col(obs(r, t, k));
}
tmp = sum(alpha);
ll(k) += log(tmp);
alpha /= tmp;
}
}
return wrap(ll);
}
QUIC_SVD::QUIC_SVD(const arma::mat& dataset,
arma::mat& u,
arma::mat& v,
arma::mat& sigma,
const double epsilon,
const double delta) :
dataset(dataset)
{
// Since columns are sample in the implementation, the matrix is transposed if
// necessary for maximum speedup.
CosineTree* ctree;
if (dataset.n_cols > dataset.n_rows)
ctree = new CosineTree(dataset, epsilon, delta);
else
ctree = new CosineTree(dataset.t(), epsilon, delta);
// Get subspace basis by creating the cosine tree.
ctree->GetFinalBasis(basis);
// Use the ExtractSVD algorithm mentioned in the paper to extract the SVD of
// the original dataset in the obtained subspace.
ExtractSVD(u, v, sigma);
}
// // [[Rcpp::export()]]
arma::mat getEx2x2(const arma::mat &Ex,
const arma::mat &Vx,
const int N,
const int D
) {
arma::mat Ex2x2(D + 1, D + 1, arma::fill::zeros) ;
arma::mat tmp(D, D) ;
tmp.fill(N) ;
arma::mat S = tmp % Vx + Ex.t() * Ex ;
// S.print("S") ;
// (tmp % Vx).print("tmp") ;
Ex2x2(0, 0) = N ;
Ex2x2.submat(1, 1, D, D) = S ;
arma::mat sums = sum(Ex, 0) ;
for (int d = 0; d < D ; d++) {
Ex2x2(d + 1, 0) = sums(0,d) ;
Ex2x2(0, d + 1) = sums(0,d) ;
}
return(Ex2x2) ;
}
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
arma::mat FFBS(int t_T, double a2, arma::vec delta, arma::vec m0, arma::mat C0, Rcpp::List FF, arma::mat GG, Rcpp::List Eta_k) {
int p = C0.n_rows;
//create vectors for m, a
arma::mat Alpha_k(p,t_T);
arma::mat m(p,t_T);
arma::mat a(p,t_T);
Rcpp::List C;
Rcpp::List R_inv;
double a2_inv = (1.0/a2);
for(int t = 0; t<t_T; t++) {
arma::mat F_t = FF[t];
arma::vec Eta_kt = Eta_k[t];
arma::mat P_star(p,p);
if(t == 0 ) {
a.col(t) = GG*m0;
P_star = GG*C0*GG.t();
} else {
arma::mat C_tm1 = C[t - 1];
a.col(t) = GG*m.col(t - 1);
P_star = GG*C_tm1*GG.t();
}
//Rcpp::Rcout << "C_{t-1}: " << P_star << std::endl;
arma::mat P_inv = P_star.i();
arma::vec f_t = F_t * a.col(t);
arma::mat R_t = P_star; //if i were to think about not discounting it would be here R_t = P_t + W_t
R_t.diag() = R_t.diag() + delta;
arma::mat R_t_inv = R_t.i();
R_inv.push_back( R_t_inv ); // and here. W_t = diag( (1-delta)/delta C_{t-1}[1,1], .00001)
//Rcpp::Rcout << "R_t: " << R_t << std::endl;
arma::mat Q_t = F_t * R_t * F_t.t();
Q_t.diag() = Q_t.diag() + a2;
//Woodbury Sherman Matrix Inversion
arma::mat Q_inv_t = - a2_inv * F_t * arma::inv(R_t_inv + a2_inv * F_t.t() * F_t ) * a2_inv * F_t.t();
Q_inv_t.diag() = Q_inv_t.diag() + a2_inv;
arma::mat A_t = R_t * F_t.t() * Q_inv_t;
//Rcpp::Rcout << "A_t: " << A_t << std::endl;
//Rcpp::Rcout << "R_t: " << R_t << std::endl;
arma::mat C_t = R_t - A_t * Q_t * A_t.t();
C.push_back(C_t);
m.col(t) = a.col(t) + A_t * (Eta_kt - f_t );
}
//now do backward sampling
for(int t = (t_T - 1); t>=0; t--) {
arma::mat C_t = C[t];
if(t == (t_T - 1) ) {
Alpha_k.col(t) = m.col(t) + arma::trans( arma::randn(1,p) * arma::chol(C_t) );
} else {
arma::mat R_inv_tp1 = R_inv[t + 1];
arma::vec b = m.col(t) + C_t*GG.t()* R_inv_tp1 * (Alpha_k.col(t + 1) - a.col( t + 1) );
arma::mat B = C_t - C_t*GG.t()*R_inv_tp1*GG*C_t;
Alpha_k.col(t) = b + arma::trans( arma::randn(1,p) * arma::chol(B) );
}
}//end of backward sampling
return Alpha_k;
}
// **********************************************************//
// Transpose //
// **********************************************************//
// [[Rcpp::export]]
arma::mat transpose (arma::mat x) {
return x.t();
}
void RandomizedSVD::Apply(const arma::mat& data,
arma::mat& u,
arma::vec& s,
arma::mat& v,
const size_t rank)
{
if (iteratedPower == 0)
iteratedPower = rank + 2;
// Center the data into a temporary matrix.
arma::vec rowMean = arma::sum(data, 1) / data.n_cols;
arma::mat R, Q, Qdata;
ann::RandomInitialization randomInit;
// Apply the centered data matrix to a random matrix, obtaining Q.
if (data.n_cols >= data.n_rows)
{
randomInit.Initialize(R, data.n_rows, iteratedPower);
Q = (data.t() * R) - arma::repmat(arma::trans(R.t() * rowMean),
data.n_cols, 1);
}
else
{
randomInit.Initialize(R, data.n_cols, iteratedPower);
Q = (data * R) - (rowMean * (arma::ones(1, data.n_cols) * R));
}
// Form a matrix Q whose columns constitute a
// well-conditioned basis for the columns of the earlier Q.
if (maxIterations == 0)
{
arma::qr_econ(Q, v, Q);
}
else
{
arma::lu(Q, v, Q);
}
// Perform normalized power iterations.
for (size_t i = 0; i < maxIterations; ++i)
{
if (data.n_cols >= data.n_rows)
{
Q = (data * Q) - rowMean * (arma::ones(1, data.n_cols) * Q);
arma::lu(Q, v, Q);
Q = (data.t() * Q) - arma::repmat(rowMean.t() * Q, data.n_cols, 1);
}
else
{
Q = (data.t() * Q) - arma::repmat(rowMean.t() * Q, data.n_cols, 1);
arma::lu(Q, v, Q);
Q = (data * Q) - (rowMean * (arma::ones(1, data.n_cols) * Q));
}
// Computing the LU decomposition is more efficient than computing the QR
// decomposition, so we only use in the last iteration, a pivoted QR
// decomposition which renormalizes Q, ensuring that the columns of Q are
// orthonormal.
if (i < (maxIterations - 1))
{
arma::lu(Q, v, Q);
}
else
{
arma::qr_econ(Q, v, Q);
}
}
// Do economical singular value decomposition and compute only the
// approximations of the left singular vectors by using the centered data
// applied to Q.
if (data.n_cols >= data.n_rows)
{
Qdata = (data * Q) - rowMean * (arma::ones(1, data.n_cols) * Q);
arma::svd_econ(u, s, v, Qdata);
v = Q * v;
}
else
{
Qdata = (Q.t() * data) - arma::repmat(Q.t() * rowMean, 1, data.n_cols);
arma::svd_econ(u, s, v, Qdata);
u = Q * u;
}
}
/* Set and get methods for the Kalman filter */
void kalmanFilter::setTransistion(arma::mat T) {
transistionMatrix = T;
transistionMatrixT = T.t();
}
int main()
{
// LOAD DATA
arma::mat X;
// A) Toy Data
// char inputFile[] = "../data_files/toyclusters/toyclusters.dat";
// B) X4.dat
//char inputFile[] = "./X4.dat";
// C) fisher data
//char inputFile[] = "./fisher.dat";
// D) MNIST data
//char inputFile[] = "../data_files/MNIST/MNIST.dat";
// E) Reduced MNIST (5000x400)
//char inputFile[] = "../data_files/MNIST/MNISTreduced.dat";
// F) Reduced MNIST (0 and 1) (1000x400)
//char inputFile[] = "../data_files/MNIST/MNISTlittle.dat";
// G) Girl.png (512x768, RGB, already unrolled)
//char inputFile[] = "girl.dat";
// H) Pool.png (383x512, RGB, already unrolled)
//char inputFile[] = "pool.dat";
// I) Cat.png (733x490, RGB, unrolled)
//char inputFile[] = "cat.dat";
// J) Airplane.png (512x512, RGB, unrolled)
//char inputFile[] = "airplane.dat";
// K) Monarch.png (512x768, RGB, unrolled)
//char inputFile[] = "monarch.dat";
// L) tulips.png (512x768 ,RGB, unrolled)
//char inputFile[] = "tulips.dat";
// M) demo.dat (2d data)
char inputFile[] = "demo.dat";
// INITIALIZE PARAMETERS
X.load(inputFile);
const arma::uword N = X.n_rows;
const arma::uword D = X.n_cols;
arma::umat ids(N,1); // needed to shuffle indices later
arma::umat shuffled_ids(N,1);
for (arma::uword i = 0; i < N; ++i) {
ids(i,0) = i;
}
arma::arma_rng::set_seed_random(); // set arma rng
// int seed = time(NULL); // set RNG seed to current time
// srand(seed);
arma::uword initial_K = 32; // initial number of clusters
arma::uword K = initial_K;
arma::umat clusters(N,1); // contains cluster assignments for each data point
for (arma::uword i = 0; i < N; ++i) {
clusters(i, 0) = i%K; // initialize as [0,1,...,K-1,0,1,...,K-1,0,...]
}
arma::umat cluster_sizes(N,1,arma::fill::zeros); // contains num data points in cluster k
for (arma::uword i = 0; i < N; ++i) {
cluster_sizes(clusters(i,0), 0) += 1;
}
arma::mat mu(N, D, arma::fill::zeros); // contains cluster mean parameters
arma::mat filler(D,D,arma::fill::eye);
std::vector<arma::mat> sigma(N,filler); // contains cluster covariance parameters
if (K < N) { // set parameters not belonging to any cluster to -999
mu.rows(K,N-1).fill(-999);
for (arma::uword k = K; k < N; ++k) {
sigma[k].fill(-999);
}
}
arma::umat uword_dummy(1,1); // dummy 1x1 matrix;
// for (arma::uword i = 0; i <N; ++i) {
// std::cout << sigma[i] << std::endl;
// }
// std::cout << X << std::endl
// << N << std::endl
// << D << std::endl
// << K << std::endl
// << clusters << std::endl
// << cluster_sizes << std::endl
// << ids << std::endl;
// INITIALIZE HYPER PARAMETERS
// Dirichlet Process concentration parameter is alpha:
double alpha = 1;
// Dirichlet Process base distribution (i.e. prior) is
// H(mu,sigma) = NIW(mu,Sigma|m_0,k_0,S_0,nu_0) = N(mu|m_0,Sigma/k_0)IW(Sigma|S_0,nu_0)
arma::mat perturbation(D,D,arma::fill::eye);
perturbation *= 0.000001;
//const arma::mat S_0 = arma::cov(X,X,1) + perturbation; // S_xbar / N
const arma::mat S_0(D,D,arma::fill::eye);
const double nu_0 = D + 2;
const arma::mat m_0 = mean(X).t();
const double k_0 = 0.01;
// std::cout << "S_0" << S_0 << std::endl;
// std::cout << S_0 << std::endl
// << nu_0 << std::endl
// << m_0 << std::endl
// << k_0 << std::endl;
// INITIALIZE SAMPLING PARAMETERS
arma::uword NUM_SWEEPS = 250; // number of Gibbs iterations
bool SAVE_CHAIN = false; // save output of each Gibbs iteration?
// arma::uword BURN_IN = NUM_SWEEPS - 10;
// arma::uword CHAINSIZE = NUM_SWEEPS - BURN_IN;
// std::vector<arma::uword> chain_K(CHAINSIZE, K); // Initialize chain variable to initial parameters for convinience
// std::vector<arma::umat> chain_clusters(CHAINSIZE, clusters);
// std::vector<arma::umat> chain_clusterSizes(CHAINSIZE, cluster_sizes);
// std::vector<arma::mat> chain_mu(CHAINSIZE, mu);
// std::vector<std::vector<arma::mat> > chain_sigma(CHAINSIZE, sigma);
// for (arma::uword sweep = 0; sweep < CHAINSIZE; ++sweep) {
// std::cout << sweep << " K\n" << chain_K[sweep] << std::endl
// << sweep << " clusters\n" << chain_clusters[sweep] << std::endl
// << sweep << " sizes\n" << chain_clusterSizes[sweep] << std::endl
// << sweep << " mu\n" << chain_mu[sweep] << std::endl;
// for (arma::uword i = 0; i < N; ++i) {
// std::cout << sweep << " " << i << " sigma\n" << chain_sigma[sweep][i] << std::endl;
// }
// }
// START CHAIN
std::cout << "Starting Algorithm with K = " << K << std::endl;
for (arma::uword sweep = 0; sweep < NUM_SWEEPS; ++sweep) {
// shuffle indices
shuffled_ids = shuffle(ids);
// std::cout << shuffled_ids << std::endl;
// SAMPLE CLUSTERS
for (arma::uword j = 0; j < N; ++j){
// std::cout << "j = " << j << std::endl;
arma::uword i = shuffled_ids(j);
arma::mat x = X.row(i).t(); // current data point
// Remove i's statistics and any empty clusters
arma::uword c = clusters(i,0); // current cluster
cluster_sizes(c,0) -= 1;
//std::cout << "old c = " << c << std::endl;
if (cluster_sizes(c,0) == 0) { // remove empty cluster
cluster_sizes(c,0) = cluster_sizes(K-1,0); // move entries for K onto position c
mu.row(c) = mu.row(K-1);
sigma[c] = sigma[K-1];
uword_dummy(0,0) = c;
arma::uvec idx = find(clusters == K - 1);
clusters.each_row(idx) = uword_dummy;
cluster_sizes(K-1,0) = 0;
mu.row(K-1).fill(-999);
sigma[K-1].fill(-999);
--K;
}
// quick test of logMvnPdf:
// arma::mat m_(2,1);
// arma::mat s_(2,2);
// arma::mat t_(2,1);
// m_ << 1 << arma::endr << 2;
// s_ << 3 << -0.2 << arma::endr << -0.2 << 1;
// t_ << -3 << arma::endr << -3;
// double lpdf = logMvnPdf(t_, m_, s_);
// std::cout << lpdf << std::endl; // śhould be -19.1034 (works)
// Find categorical distribution over clusters (tested)
arma::mat logP(K+1, 1, arma::fill::zeros);
// quick test of logInvWishPdf
// arma::mat si_(2,2), s_(2,2);
// double nu_ = 4;
// si_ << 1 << 0.5 << arma::endr << 0.5 << 4;
// s_ << 3 << -0.2 << arma::endr << -0.2 << 1;
// double lpdf = logInvWishPdf(si_, s_, nu_);
// std::cout << lpdf << std::endl; // should be -7.4399 (it is)
// quick test for logNormInvWishPdf
// arma::mat si_(2,2), s_(2,2);
// arma :: mat mu_(2,1), m_(2,1);
// double k_ = 0.5, nu_ = 4;
// si_ << 1 << 0.5 << arma::endr << 0.5 << 4;
// s_ << 3 << -0.2 << arma::endr << -0.2 << 1;
// mu_ << -3 << arma::endr << -3;
// m_ << 1 << arma::endr << 2;
// double lp = logNormInvWishPdf(mu_,si_,m_,k_,s_,nu_);
// std::cout << lp << std::endl; // should equal -15.2318 (it is)
// p(existing clusters) (tested)
for (arma::uword k = 0; k < K; ++k) {
arma::mat m_ = mu.row(k).t();
arma::mat s_ = sigma[k];
logP(k,0) = log(cluster_sizes(k,0)) - log(N-1+alpha) + logMvnPdf(x,m_,s_);
}
// p(new cluster): find partition function (tested)
// arma::mat dummy_mu(D, 1, arma::fill::zeros);
// arma::mat dummy_sigma(D, D, arma::fill::eye);
// double logPrior, logLklihd, logPstr, logPartition;
// posterior hyperparameters (tested)
arma::mat m_1(D,1), S_1(D,D);
double k_1, nu_1;
k_1 = k_0 + 1;
nu_1 = nu_0 + 1;
m_1 = (k_0*m_0 + x) / k_1;
S_1 = S_0 + x * x.t() + k_0 * (m_0 * m_0.t()) - k_1 * (m_1 * m_1.t());
// std::cout << k_1 << std::endl
// << nu_1 << std::endl
// << m_1 << std::endl
// << S_1 << std::endl;
// // partition = likelihood*prior/posterior (tested)
// // (perhaps a direct computation of the partition function would be better)
// logPrior = logNormInvWishPdf(dummy_mu, dummy_sigma, m_0, k_0, S_0, nu_0);
// logLklihd = logMvnPdf(x, dummy_mu, dummy_sigma);
// logPstr = logNormInvWishPdf(dummy_mu, dummy_sigma, m_1, k_1, S_1, nu_1);
// logPartition = logPrior + logLklihd - logPstr;
// std::cout << "log Prior = " << logPrior << std::endl
// << "log Likelihood = " << logLklihd << std::endl
// << "log Posterior = " << logPstr << std::endl
// << "log Partition = " << logPartition << std::endl;
// Computing partition directly
double logS0,signS0,logS1,signS1;
arma::log_det(logS0,signS0,S_0);
arma::log_det(logS1,signS1,S_1);
/*std::cout << "log(det(S_0)) = " << logS0 << std::endl
<< "log(det(S_1)) = " << logS1 << std::endl;*/
double term1 = 0.5*D*(log(k_0)-log(k_1));
double term2 = -0.5*D*log(arma::datum::pi);
double term3 = 0.5*(nu_0*logS0 - nu_1*logS1);
double term4 = lgamma(0.5*nu_1);
double term5 = -lgamma(0.5*(nu_1-D));
double logPartition = term1+term2+term3+term4+term5;
/*double logPartition = 0.5*D*(log(k_0)-log(k_1)-log(arma::datum::pi)) \
/+0.5*(nu_0*logS0 - nu_1*logS1) + lgamma(0.5*nu_1) - lgamma(0.5*(nu_1-D));*/
/* std::cout << "term1 = " << term1 << std::endl
<< "term2 = " << term2 << std::endl
<< "term3 = " << term3 << std::endl
<< "term4 = " << term4 << std::endl
<< "term5 = " << term5 << std::endl;*/
//std::cout << "logP = " << logPartition << std::endl;
// p(new cluster): (tested)
logP(K,0) = log(alpha) - log(N - 1 + alpha) + logPartition;
// std::cout << "logP(new cluster) = " << logP(K,0) << std::endl;
//if(i == 49)
//assert(false);
// sample cluster for i
arma::uword c_ = logCatRnd(logP);
clusters(i,0) = c_;
//if (j % 10 == 0){
//std::cout << "New c = " << c_ << std::endl;
//std::cout << "logP = \n" << logP << std::endl;
//}
// quick test for mvnRnd
// arma::mat mu, si;
// mu << 1 << arma::endr << 2;
// si << 1 << 0.9 << arma::endr << 0.9 << 1;
// arma::mat m = mvnRnd(mu, si);
// std::cout << m << std::endl;
// quick test for invWishRnd
// double df = 4;
// arma::mat si(2,2);
// si << 1 << 1 << arma::endr << 1 << 1;
// arma::mat S = invWishRnd(si,df);
// std::cout << S << std::endl;
if (c_ == K) { // Sample parameters for any new-born clusters from posterior
cluster_sizes(K, 0) = 1;
arma::mat si_ = invWishRnd(S_1, nu_1);
//arma::mat si_ = S_1;
arma::mat mu_ = mvnRnd(m_1, si_/k_1);
//arma::mat mu_ = m_1;
mu.row(K) = mu_.t();
sigma[K] = si_;
K += 1;
} else {
cluster_sizes(c_,0) += 1;
}
// if (sweep == 0)
// std::cout << " K = " << K << std::endl;
// // if (j == N-1) {
// // std::cout << logP << std::endl;
// // std::cout << K << std::endl;
// // assert(false);
// // }
// std::cout << "K = " << K << "\n" << std::endl;
}
// sample CLUSTER PARAMETERS FROM POSTERIOR
for (arma::uword k = 0; k < K; ++k) {
// std::cout << "k = " << k << std::endl;
// cluster data
arma::mat Xk = X.rows(find(clusters == k));
arma::uword Nk = cluster_sizes(k,0);
// posterior hyperparameters
arma::mat m_Nk(D,1), S_Nk(D,D);
double k_Nk, nu_Nk;
arma::mat sum_k = sum(Xk,0).t();
arma::mat cov_k(D, D, arma::fill::zeros);
for (arma::uword l = 0; l < Nk; ++l) {
cov_k += Xk.row(l).t() * Xk.row(l);
}
k_Nk = k_0 + Nk;
nu_Nk = nu_0 + Nk;
m_Nk = (k_0 * m_0 + sum_k) / k_Nk;
S_Nk = S_0 + cov_k + k_0 * (m_0 * m_0.t()) - k_Nk * (m_Nk * m_Nk.t());
// sample fresh parameters
arma::mat si_ = invWishRnd(S_Nk, nu_Nk);
//arma::mat si_ = S_Nk;
arma::mat mu_ = mvnRnd(m_Nk, si_/k_Nk);
//arma::mat mu_ = m_Nk;
mu.row(k) = mu_.t();
sigma[k] = si_;
}
std::cout << "Iteration " << sweep + 1 << "/" << NUM_SWEEPS<< " done. K = " << K << std::endl;
// // STORE CHAIN
// if (SAVE_CHAIN) {
// if (sweep >= BURN_IN) {
// chain_K[sweep - BURN_IN] = K;
// chain_clusters[sweep - BURN_IN] = clusters;
// chain_clusterSizes[sweep - BURN_IN] = cluster_sizes;
// chain_mu[sweep - BURN_IN] = mu;
// chain_sigma[sweep - BURN_IN] = sigma;
// }
// }
}
std::cout << "Final cluster sizes: " << std::endl
<< cluster_sizes.rows(0, K-1) << std::endl;
// WRITE OUPUT DATA TO FILE
arma::mat MU = mu.rows(0,K-1);
arma::mat SIGMA(D*K,D);
for (arma::uword k = 0; k < K; ++k) {
SIGMA.rows(k*D,(k+1)*D-1) = sigma[k];
}
arma::umat IDX = clusters;
// A) toycluster data
// char MuFile[] = "../data_files/toyclusters/dpmMU.out";
// char SigmaFile[] = "../data_files/toyclusters/dpmSIGMA.out";
// char IdxFile[] = "../data_files/toyclusters/dpmIDX.out";
// B) X4.dat
char MuFile[] = "dpmMU.out";
char SigmaFile[] = "dpmSIGMA.out";
char IdxFile[] = "dpmIDX.out";
std::ofstream KFile("K.out");
MU.save(MuFile, arma::raw_ascii);
SIGMA.save(SigmaFile, arma::raw_ascii);
IDX.save(IdxFile, arma::raw_ascii);
KFile << "K = " << K << std::endl;
if (SAVE_CHAIN) {}
// std::ofstream chainKFile("chainK.out");
// std::ofstream chainClustersFile("chainClusters.out");
// std::ofstream chainClusterSizesFile("chainClusterSizes.out");
// std::ofstream chainMuFile("chainMu.out");
// std::ofstream chainSigmaFile("chainSigma.out");
// chainKFile << "Dirichlet Process Mixture Model.\nInput: " << inputFile << std::endl
// << "Number of iterations of Gibbs Sampler: " << NUM_SWEEPS << std::endl
// << "Burn-In: " << BURN_IN << std::endl
// << "Initial number of clusters: " << initial_K << std::endl
// << "Output: Number of cluster (K)\n" << std::endl;
// chainClustersFile << "Dirichlet Process Mixture Model.\nInput: " << inputFile << std::endl
// << "Number of iterations of Gibbs Sampler: " << NUM_SWEEPS << std::endl
// << "Burn-In: " << BURN_IN << std::endl
// << "Initial number of clusters: " << initial_K << std::endl
// << "Output: Cluster identities (clusters)\n" << std::endl;
// chainClusterSizesFile << "Dirichlet Process Mixture Model.\nInput: " << inputFile << std::endl
// << "Number of iterations of Gibbs Sampler: " << NUM_SWEEPS << std::endl
// << "Burn-In: " << BURN_IN << std::endl
// << "Initial number of clusters: " << initial_K << std::endl
// << "Output: Size of clusters (cluster_sizes)\n" << std::endl;
// chainMuFile << "Dirichlet Process Mixture Model.\nInput: " << inputFile << std::endl
// << "Number of iterations of Gibbs Sampler: " << NUM_SWEEPS << std::endl
// << "Burn-In: " << BURN_IN << std::endl
// << "Initial number of clusters: " << initial_K << std::endl
// << "Output: Samples for cluster mean parameters (mu. Note: means stored in rows)\n" << std::endl;
// chainSigmaFile << "Dirichlet Process Mixture Model.\nInput: " << inputFile << std::endl
// << "Number of iterations of Gibbs Sampler: " << NUM_SWEEPS << std::endl
// << "Burn-In " << BURN_IN << std::endl
// << "Initial number of clusters: " << initial_K << std::endl
// << "Output: Samples for cluster covariances (sigma)\n" << std::endl;
// for (arma::uword sweep = 0; sweep < CHAINSIZE; ++sweep) {
// arma::uword K = chain_K[sweep];
// chainKFile << "Sweep #" << BURN_IN + sweep + 1 << "\n" << chain_K[sweep] << std::endl;
// chainClustersFile << "Sweep #" << BURN_IN + sweep + 1 << "\n" << chain_clusters[sweep] << std::endl;
// chainClusterSizesFile << "Sweep #" << BURN_IN + sweep + 1 << "\n" << chain_clusterSizes[sweep].rows(0, K - 1) << std::endl;
// chainMuFile << "Sweep #" << BURN_IN + sweep + 1 << "\n" << chain_mu[sweep].rows(0, K - 1) << std::endl;
// chainSigmaFile << "Sweep #" << BURN_IN + sweep + 1<< "\n";
// for (arma::uword i = 0; i < K; ++i) {
// chainSigmaFile << chain_sigma[sweep][i] << std::endl;
// }
// chainSigmaFile << std::endl;
// }
// }
return 0;
}
// The number of users should always be a positive integer.
// The number of movies should always be a positive integer.
// The number of features should always be a positive integer.
int CollaborativeFiltering::ComputeGradient(const DataUnlabeled &ratings_data,
const DataUnlabeled &indicator_data,int num_users,int num_movies,
int num_features) {
assert(num_users >= 1);
assert(num_movies >= 1);
assert(num_features >= 1);
const int kTotalNumFeatures = num_features*(num_users+num_movies);
const arma::vec kCurrentTheta = theta();
arma::mat features_cvec = arma::zeros<arma::mat>(num_movies*num_features,1);
arma::mat params_cvec = arma::zeros<arma::mat>(num_users*num_features,1);
for(int feature_index=0; feature_index<kTotalNumFeatures; feature_index++)
{
if (feature_index < (num_users*num_features)) {
params_cvec(feature_index) = kCurrentTheta[feature_index];
}
else {
features_cvec(feature_index-(num_users*num_features)) = \
kCurrentTheta[feature_index];
}
}
arma::mat features_cvec_squared = arma::square(features_cvec);
arma::mat params_cvec_squared = arma::square(params_cvec);
arma::mat params_mat = arma::reshape(params_cvec,num_users,num_features);
arma::mat features_mat = \
arma::reshape(features_cvec,num_movies,num_features);
const arma::mat kSubsetIndicatorMat = \
indicator_data.training_features().submat(0,0,num_movies-1,num_users-1);
const arma::mat kSubsetRatingsMat = \
ratings_data.training_features().submat(0,0,num_movies-1,num_users-1);
const arma::mat kYMat = \
(arma::ones<arma::mat>(num_users,num_movies)-kSubsetIndicatorMat.t()) % \
(params_mat*features_mat.t())+kSubsetRatingsMat.t();
const arma::mat kDiffMat = (params_mat*features_mat.t()-kYMat).t();
arma::mat grad_params_arr = arma::zeros<arma::mat>(num_users*num_features,1);
arma::mat grad_params_arr_reg = \
arma::zeros<arma::mat>(num_users*num_features,1);
for(int grad_index=0; grad_index<(num_users*num_features); grad_index++)
{
int user_index = 1+(grad_index % num_users);
int feature_index = 1+((grad_index-(grad_index % num_users))/num_users);
grad_params_arr(grad_index) = \
arma::as_scalar(sum(kDiffMat.col(user_index-1) % \
features_mat.col(feature_index-1)));
grad_params_arr_reg(grad_index) = \
grad_params_arr(grad_index)+lambda_*params_cvec(grad_index);
}
arma::mat grad_features_arr = \
arma::zeros<arma::mat>(num_movies*num_features,1);
arma::mat grad_features_arr_reg = \
arma::zeros<arma::mat>(num_movies*num_features,1);
for(int grad_index=0; grad_index<(num_movies*num_features); grad_index++)
{
int movie_index = 1+(grad_index % num_movies);
int feature_index = 1+((grad_index-(grad_index % num_movies))/num_movies);
grad_features_arr(grad_index) = \
arma::as_scalar(sum(kDiffMat.row(movie_index-1) % \
(params_mat.col(feature_index-1)).t()));
grad_features_arr_reg(grad_index) = \
grad_features_arr(grad_index)+lambda_*features_cvec(grad_index);
}
arma::vec gradient_array_reg = arma::zeros<arma::vec>(kTotalNumFeatures);
gradient_array_reg.subvec(0,(num_users*num_features-1)) = \
grad_params_arr_reg;
gradient_array_reg.subvec(num_users*num_features,kTotalNumFeatures-1) = \
grad_features_arr_reg;
set_gradient(gradient_array_reg);
return 0;
}
/** Internal function that gives the output in c++ way (writes into allocated memory).
* See glm_ridge_c for a wrapper that is being called from R.
*/
void glm_ridge( vec& beta, // output: regression coefficients (contains intercept)
double& loss, // output: value of the loss function
vec& w, // output: weights of the pseudo-gaussian observations at the optimum (needed for Student-t model)
int& qau, // output: number of quadratic approximation updates
arma::mat x,
Function pseudo_obs,
double lambda,
bool intercept,
arma::vec penalty, // relative penalties for the variables
double thresh,
int qa_updates_max,
int ls_iter_max=50,
bool debug=false)
{
if (intercept) {
// add a vector of ones to x and set zero penalty for the intercept
x = join_horiz(ones<vec>(x.n_rows), x);
penalty = join_vert(zeros<vec>(1), penalty);
}
int n = x.n_rows;
int D = x.n_cols;
int ls_iter; // counts linesearch iterations
int j;
double t; // step size in line search
double a = 0.1; // backtracking line search parameters a and b (see Boyd and Vandenberghe, 2004)
double b = 0.5;
// initialization
vec beta_new(D); beta_new.zeros();
vec dbeta(D); dbeta.zeros();
vec grad(D); grad.zeros(); // gradient of the negative log likelihood w.r.t. the regression coefficients
vec grad_f(n); grad_f.zeros(); // pointwise gradient of the negative log likelihood w.r.t. the latent values f
vec f = x*beta;
mat xw(n,D); // this will be the weighted x
mat regmat = lambda*diagmat(penalty);//eye(D,D); // regularization matrix
// initial quadratic approximation
List obs = pseudo_obs(f,w);
vec z = as<vec>(obs["z"]);
w = as<vec>(obs["w"]);
grad_f = as<vec>(obs["grad"]);
double loss_initial = ((double) obs["loss"]) + elnet_penalty(beta, lambda, 0, penalty);
double loss_old = loss_initial; // will be updated iteratively
loss = loss_initial; // will be updated iteratively
double tol = thresh*fabs(loss_initial); // threshold for convergence
double decrement = 0; // newton decrement, used to monitor convergence
qau = 0;
while (qau < qa_updates_max) {
// weight the observations
for (j=0; j<D; ++j)
xw.col(j) = x.col(j) % sqrt(w);
// weighted least squares solution
beta_new = solve( xw.t()*xw + regmat, xw.t()*(sqrt(w)%z) );
dbeta = beta_new - beta;
grad = x.t()*grad_f + lambda*penalty%beta; // gradient of negative log likelihood + gradient of penalty
decrement = -sum(grad%dbeta); // newton decrement
// check for convergence
if (decrement < tol)
break;
// backtracking line search
t = 1.0/b;
ls_iter = 0;
while (ls_iter < ls_iter_max) {
t = b*t;
f = x*(beta+t*dbeta);
obs = pseudo_obs(f,w);
loss = ((double) obs["loss"]) + elnet_penalty(beta+t*dbeta, lambda, 0, penalty);
++ls_iter;
if (std::isnan(loss))
continue;
if (decrement > 0) {
if (loss < loss_old - a*t*decrement )
break;
} else {
Rcpp::Rcout << "The search direction is not a descent direction ";
Rcpp::Rcout << "(newton decrement = " << decrement << ", should be positive), ";
Rcpp::Rcout << ", this is likely a bug. Please report to the developers." << '\n';
}
}
if (ls_iter == ls_iter_max && ls_iter_max > 1) {
// beta.print("beta = ");
// dbeta.print("dbeta = ");
// grad.print("grad = ");
// Rcpp::Rcout << "loss = " << loss << "\n";
// Rcpp::Rcout << "loss_initial = " << loss_initial << "\n";
// Rcpp::Rcout << "tol = " << tol << "\n";
// Rcpp::Rcout << "decrement = " << decrement << "\n";
// Rcpp::Rcout << "\n\n";
Rcpp::Rcout << "glm_ridge warning: maximum number of line search iterations reached. The optimization can be ill-behaved.\n";
break;
}
// update the solution
beta = beta + t*dbeta;
z = as<vec>(obs["z"]);
w = as<vec>(obs["w"]);
grad_f = as<vec>(obs["grad"]);
loss_old = loss;
++qau;
}
if (qau == qa_updates_max && qa_updates_max > 1) {
if (decrement/fabs(loss_initial) > 100*tol) {
// warn the user if the max number of iterations is reached and we are relatively far
// (two orders of magnitude) from the given convergence threshold
Rcpp::Rcout << "glm_ridge warning: maximum number of quadratic approximation updates reached, within ";
Rcpp::Rcout << decrement << " from optimum (tolerance = " << thresh << ").\n";
}
}
}
// funcao FFBS para regressao com V constante e fator de desconto
Rcpp::List drmOnly1FFBSdiscW(arma::mat Y, arma::mat X, arma::mat dV, double discW,
arma::vec m0, arma::mat ZC0) {
int T = Y.n_rows; // ATENCAO: matriz de dados deve entrar T x q!!
int q = Y.n_cols;
int r = q*X.n_cols; // ATENCAO: matriz de exogenas deve entrar sendo T x p
mat Yt = Y.t();
mat I_q = diagmat(ones(q));
// FORWARD FILTERING
mat mm(r, T+1);
vec aa(r);//nao e' preciso armazenar aa_t
mat RR(r, r);//nao e' preciso armazenar RR_t
vec ff(q); //nao e' preciso armazenar ff
mat QQ(q, q); //nao e' preciso armazenar seus valores
mat AA;
mat ee;
mat FF;
//para previsao, e' preciso armazenar W_{T+1}
mat dVInv = inv(dV);
//parametros para forma quadrada
mat ZR;
mat ZC(r, r); //utilizado para fazer a amostragem retrospectiva
//objetos para decomposicao em valores singulares e espectral
mat L, Eigvec;
vec eigval;
double sqrtDiscW = sqrt(discW);
double sqrt1mDiscW = sqrt(1-discW);
//para evitar o loop da amostragem retrospectiva, recorri a uma propriedade
//do FFBS com o uso do fator de desconto.
//O que observei e' que
//th_{t-k} = (1-delta) \sum delta^j m_{t-k+j} + delta^k m_T + \sum delta^j e_{T-k+j}
//IntegerVector seq0toT = seq_len(T+1)-1;
//vec powDiscW = exp(log(discW)*as<NumericVector>(seq0toT));
//mat Dmat(T+1, T+1); Dmat.zeros();
//valores aleatorios gerados
mat th = randn(r, T+1);
mm.col(0) = m0;
ZC = ZC0;
th.col(0) = sqrt1mDiscW*ZC*th.col(0);
//Dmat.submat(0, 0, T, 0) = powDiscW.subvec(0, T);
for (int k = 1; k < (T+1); k++) {
//evolucao
aa = mm.col(k-1);
ZR = ZC/sqrtDiscW;
RR = ZR * ZR.t();
//predicao
FF = kron(I_q, X.row(k-1)).t();
ff = FF.t()*aa;
QQ = symmatu(FF.t() * RR * FF + dV);
//atualizacao
L = ZR.t()*FF; //forma raiz quadrada
eig_sym(eigval, Eigvec, L * dVInv * L.t());
ZC = ZR * Eigvec * diagmat(1.0/sqrt(eigval + 1.0));
AA = ZC*ZC.t()*FF*dVInv; //p.105 West & Harrison (1997)
ee = Yt.col(k-1) - ff;
mm.col(k) = aa + AA*ee;
th.col(k) = sqrt1mDiscW*ZC*th.col(k);
mm.col(k-1) -= discW*mm.col(k-1); //mm agora representa mm*
//Dmat.submat(k, k, T, k) = powDiscW.subvec(0, T-k);
}
// BACKWARD SAMPLING
//simulacao dos estados sem loop
/*
th = (mm+th)*Dmat;
rowvec oneP = ones(X.n_cols);
mat Mu = kron(I_q, oneP) * (th.cols(1, T) % repmat(X.t(), q, 1));
*/
mat Mu(q, T);
th.col(T) += mm.col(T);
for(int k = 0; k < T; k++) {
th.col(T-1-k) += mm.col(T-1-k) + discW*th.col(T-k);
Mu.col(T-1-k) = kron(I_q, X.row(T-1-k))*th.col(T-k);
}
return Rcpp::List::create(Named("th") = th, Named("Mu") = Mu.t(),
Named("ZW") = sqrt((1-discW)/discW)*ZC);
}
// [[Rcpp::export]]
Rcpp::List getWEXPcutoff(arma::mat data, arma::mat subdata, arma::mat Y, arma::mat subY, int N, arma::mat RT_out, double predictTime, arma::vec resid_sco, double fitvar, arma::colvec cutoffs){
//create dataD
arma::mat dataDuns = data.rows(find(data.col(1)==1));
arma::mat dataD = dataDuns.rows(sort_index(dataDuns.col(0)));
int n = data.n_rows, nD = dataD.n_rows, np = Y.n_cols, ncuts = subdata.n_rows;
//guide
colvec times = data.col(0);
// status= data.col(1);
// Dtimes = dataD.col(0);
// weights = data.col(4);
// Dweights = dataD.col(4);
uvec tmpind = find((data.col(0) <= predictTime)%data.col(1)); // indices of (data$times<=predict.time)&(data$status==1)
mat myempty(1,1);
uvec tmpindT = conv_to<uvec>::from(CSumI(times.elem(tmpind), 4, dataD.col(0), myempty, FALSE));
colvec rrk = exp(data.col(6)); //data.col(6) is data$linearY
// build riskmat
mat riskmat(n, nD);
mat::iterator riskmat_it = riskmat.begin();
for(colvec::iterator j = dataD.begin_col(0); j != dataD.end_col(0); j++){
for( colvec::iterator i = data.begin_col(0); i != data.end_col(0); i++){
*riskmat_it = *i >= *j; riskmat_it++;
}
}
//s0 and s1
colvec s0 = riskmat.t()*(rrk%data.col(4));
colvec s1 = riskmat.t()*trans(Vec2Mat(rrk%data.col(4), np)%Y.t());
//haz0 and cumhaz0
colvec haz0 = dataD.col(4)/sum(riskmat%trans(Vec2Mat(rrk%data.col(4), nD))).t();
colvec cumhaz0 = cumsum(haz0);
colvec ptvec(1); ptvec(0) = predictTime;
colvec cumhaz_t0 = CSumI(ptvec, 4, dataD.col(0), haz0, TRUE);
//Wexp
colvec Wexp_beta = resid_sco*fitvar*N;
colvec WexpLam1(n); WexpLam1.zeros(n);
WexpLam1(tmpind) = N/s0(tmpindT - 1);
WexpLam1 = WexpLam1 - CSumI( myPmin(data.col(0), predictTime), 4, dataD.col(0), haz0/s0, TRUE)%rrk*N;
colvec WexpLam2 = Wexp_beta*CSumI(ptvec, 4, dataD.col(0), haz0%s1/trans(Vec2Mat(s0, np)), TRUE);
colvec WexpLam = WexpLam1 - WexpLam2;
//Fyk = Pr(Sy < c)
colvec Fyk = CSumI( cutoffs, 4, data.col(6), data.col(4), TRUE)/sum(data.col(4));
colvec dFyk(Fyk.n_elem); dFyk(0) = 0;
dFyk(span(1, Fyk.n_elem - 1)) = Fyk(span(0, Fyk.n_elem-2));
dFyk = Fyk - dFyk;
colvec Sy = subdata.col(5);
colvec Syall = data.col(5);
colvec St0_Fyk = cumsum(Sy%dFyk);
double St0 = max(St0_Fyk);
colvec St0_Syk = St0 - St0_Fyk;
//
mat Wexp_Cond_Stc = -Vec2Mat(Sy%exp(subdata.col(6)), n)%(trans(Vec2Mat(WexpLam, ncuts)) +as_scalar(cumhaz_t0)*Wexp_beta*subY.t());
mat tmpmat = conv_to<mat>::from(trans(Vec2Mat(data.col(6), ncuts)) > Vec2Mat(cutoffs, n));
mat Wexp_Stc = trans(CSumI(cutoffs, 0, subdata.col(6), Wexp_Cond_Stc.t()%Vec2Mat(dFyk, n).t(), TRUE)) + trans(Vec2Mat(Syall,ncuts))%tmpmat - Vec2Mat(St0_Syk, n);
colvec Wexp_St = sum(trans(Wexp_Cond_Stc)%trans(Vec2Mat(dFyk, n))).t() + Syall - St0;
mat Wexp_Fc = 1-tmpmat - Vec2Mat(Fyk, n);
//assemble for classic performance measures, given linear predictor
List out(8);
out[0] = -Wexp_Cond_Stc;
out[1] = Wexp_Fc;
mat Wexp_St_mat = Vec2Mat(Wexp_St, ncuts).t();
out[2] = (-Wexp_St_mat%Vec2Mat(RT_out.col(3), n) + Wexp_Stc)/St0;
out[3] = (Wexp_St_mat%Vec2Mat(RT_out.col(4), n) -Wexp_Fc - Wexp_Stc)/(1-St0);
out[4] = -Wexp_St;
out[5] = (Wexp_St_mat - Wexp_Stc - Vec2Mat(RT_out.col(6), n)%Wexp_Fc)/Vec2Mat(Fyk, n);
out[6] = (Vec2Mat(RT_out.col(5)-1, n)%Wexp_Fc - Wexp_Stc)/Vec2Mat(1-Fyk, n);
out[7] = Wexp_beta;
return out;
}
Rcpp::List irls_binomial_cpp_fast_br(arma::mat A, arma::vec b, double maxit, double tol)
{
//Def
arma::vec x;
x.zeros(A.n_cols,1);
arma::vec xold;
arma::mat varmatrix;
double nobs;
nobs = A.n_rows;
double df;
df = A.n_cols;
double n;
double ll;
double aic;
double bic;
double mdl;
arma::vec W(nobs);
arma::vec unit(nobs);
unit.ones(nobs);
arma::vec eta(nobs);
arma::vec g(nobs);
arma::vec gprime(nobs);
arma::vec z(nobs);
//mod
arma::vec bprime(nobs);
//int k;
for (int i = 0; i < maxit; ++i) {
eta = A * x;
for (int j=0; j < nobs; ++j) {
g[j] = 1.0 / (1.0 + exp(-1.0 * eta[j]));
gprime[j] = exp (-1.0 * eta[j]) / ((1.0 + exp (-1.0 * eta[j])) * (1.0 + exp (-1.0 * eta[j])));
//mod
bprime[j] = (b[j]+(df/nobs)*(0.5))/(1+(df/nobs));
//bprime[j] = b[j]+(sum(b)/nobs)*(0.5);
}
//z = eta+(b-g)/gprime;
z = eta+(bprime-g)/gprime;
W = (gprime % gprime);
W /= (g % (unit-g));
//W += unit;
xold = x;
//coefficients
//x = arma::solve(A.t()*(W % A.each_col()), A.t()*(W % z), arma::solve_opts::no_approx);
varmatrix = A.t()*(W % A.each_col());
x = arma::solve(varmatrix, A.t()*(W % z), arma::solve_opts::no_approx);
//k = i;
if(sqrt(arma::dot(x-xold,x-xold)) < tol){
break;
}}
n = A.n_rows;
//arma::vec e;
//double ssr;
//e = (b - A*x);
//e = (bprime - A*x);
//ssr = accu(e.t()*e);
//scores
//ll = arma::accu(-arma::dot(b,log(unit + exp(-(A*x)))) - arma::dot((unit-b),log(unit + exp(A*x))));
ll = arma::accu(-arma::dot(b,log(unit + exp(-(A*x)))) - arma::dot((unit-b),log(unit + exp(A*x))));
aic = - 2 * ll + 2 * df;
bic = - 2 * ll + log(nobs) * df;
//mdl
// arma::mat xz;
// xz.zeros(size(x));
//
// arma::vec ez;
// double ssrz;
// double ssrtot;
// double RR;
// double F;
// double mdl;
// arma::vec yaverage(n);
//
// ez = (b - A*xz);
// ssrz = accu(ez.t()*ez);
// F = (((ssrz - ssr)/df)/(ssr/((n-(df + 1)))));
//
// for (int j=0; j < n; ++j) {
// yaverage[j] = b[j] - arma::mean(b);
// }
//
// ssrtot = accu(yaverage.t()*yaverage);
//
// RR = 1-(ssr/ssrtot);
//
// if (RR > (df/n)) {
// mdl = (n/2) * log(ssr/(n-df)) + (df/2) * log(F) + log(n);
// } else {
// mdl = (n/2) * log((accu(b.t()*b))/n) + 0.5 * log(n);
// }
//return
return Rcpp::List::create(
Rcpp::Named("loglik") = ll,
Rcpp::Named("aic") = aic,
Rcpp::Named("bic") = bic,
Rcpp::Named("mdl") = mdl
);
}
void kalmanFilter::setMeasurement(arma::mat M) {
measurementMatrix = M;
measurementMatrixT = M.t();
}
///
/// \brief Vespucci::Math::DimensionReduction::VCA
/// Vertex Component Analysis
/// \param R The dataset
/// \param endmembers Number of endmembers to compute
/// \param indices Row indices of pure components.
/// \param endmember_spectra Spectra of pure components (note that these are in
/// columns, not rows as in spectra_)
/// \param projected_data Projected data
/// \param fractional_abundances Purity of a given spectrum relative to endmember
/// \return Convergeance (no actual test implemented...)
///
bool Vespucci::Math::DimensionReduction::VCA(const arma::mat &R, arma::uword p,
arma::uvec &indices, arma::mat &endmember_spectra,
arma::mat &projected_data, arma::mat &fractional_abundances)
{
//Initializations
arma::uword L = R.n_rows;
arma::uword N = R.n_cols;
if (L == 0 || N == 0){
std::cerr << "No data!" << std::endl;
return false;
}
if (p > L){
std::cerr << "wrong number of endmembers (" << p << ")!"<< std::endl;
std::cerr << "set to 5 or one less than number of spectra" << std::endl;
p = (L < 5? 5: L-1);
}
//mat of SNR
arma::mat r_m = mean(R, 1);
arma::mat R_m = arma::repmat(r_m, 1, N); //the mean of each spectral band
arma::mat R_o = R - R_m; //mean-center the data
arma::mat Ud;
arma::vec Sd;
arma::mat Vd;
//arma::svds(Ud, Sd, Vd, arma::sp_mat(R_o * R_o.t()/N), p);
Vespucci::Math::DimensionReduction::svds(R_o*R_o.t()/N, p, Ud, Sd, Vd);
arma::mat x_p;
try{
x_p = Ud.t() * R_o;
}catch(std::exception e){
std::cout << "Ud.t() * R_o" << std::endl;
}
double SNR = Vespucci::Math::DimensionReduction::estimate_snr(R, r_m, x_p);
double SNR_th = 15 + 10*log10(p);
//Choose projective projection or projection to p-1 subspace
arma::mat y;
if (SNR < SNR_th){
arma::uword d = p - 1;
Ud = Ud.cols(0, d-1);
projected_data = Ud * x_p.rows(0, d-1) + R_m; //in dimension L
arma::mat x = x_p.rows(0, d-1);//x_p = trans(Ud)*R_o, p-dimensional subspace
//following three lines are one in arma::matlab...
arma::mat sum_squares = sum(pow(x, 2));
double c = sum_squares.max();
c = std::sqrt(c);
y = arma::join_vert(x, c*arma::ones(1, N));
}
else{
arma::uword d = p;
Vespucci::Math::DimensionReduction::svds(R*R.t()/N, p, Ud, Sd, Vd);
arma::svds(Ud, Sd, Vd, arma::sp_mat(R*R.t()/N), d);//R_o is a mean centered version...
x_p = Ud.t() * R;
projected_data = Ud * x_p.rows(0, d-1);
arma::mat x = Ud.t() * R;
arma::mat u = arma::mean(x, 1);
y = x / arma::repmat(sum(x % arma::repmat(u, 1, N)), d, 1);
}
// The VCA algorithm
arma::vec w;
w.set_size(p);
arma::vec f;
arma::rowvec v;
indices.set_size(p);
//there are no fill functions for arma::uvecs
for (arma::uword i = 0; i < p; ++i)
indices(i) = 0;
arma::mat A = arma::zeros(p, p);
double v_max;
double sum_squares;
arma::uvec q1;
A(p-1, 0) = 1;
for (arma::uword i = 0; i < p; ++i){
w.randu();
f = w - A*arma::pinv(A)*w;
sum_squares = sqrt(sum(square(f)));
f /= sum_squares;
v = f.t() * y;
v_max = arma::max(abs(v));
q1 = arma::find(abs(v) == v_max, 1);
indices(i) = q1(0);
A.col(i) = y.col(indices(i)); //same as x.col(indices(i));
}
endmember_spectra = projected_data.cols(indices);
fractional_abundances = arma::trans(pinv(endmember_spectra) * projected_data);
return true;
}
CVXOBJ cvxObj(double t, arma::mat Postprob, arma::rowvec wght, arma::mat x, arma::mat y, arma::mat n, arma::mat ab,
arma::mat F, arma::vec h, unsigned int N, unsigned int Nrep ){
unsigned int m = F.n_rows;
unsigned int K = Postprob.n_cols;
arma::vec d(m);
arma::mat D(m,m);
arma::mat J(2,K);
arma::mat H_d(2,K);
arma::mat H_o(2,K);
arma::mat n_ab(N,Nrep*K);
arma::mat x_a(N,Nrep*K);
arma::mat y_b(N,Nrep*K);
arma::mat dn_ab(K,K);
arma::mat dx_a(K,K);
arma::mat dy_b(K,K);
arma::mat px(N,K);
// List out(3);
double f;
arma::vec g(2*K);
arma::mat H(2*K,2*K);
J.zeros();
H_d.zeros();
H_o.zeros();
d = F * vectorise(ab) - h;
D = diagmat(1 / d);
n_ab = N_ab(n,sum(ab,0));
x_a = N_ab(x,ab.row(0));
y_b = N_ab(y,ab.row(1));
J =mydigamma( ones(2,1) * sum(ab,0) ) % (ones(2,1)*wght) * Nrep;
cmpDgm(N_ab(n,sum(ab,0)),K).t() * Postprob;
mydigamma(ab) % (ones(2,1)*wght) *Nrep;
dn_ab = cmpDgm(n_ab,K).t() * Postprob;
dx_a = cmpDgm(x_a,K) .t() * Postprob;
dy_b = cmpDgm(y_b,K) .t() * Postprob;
J =mydigamma( ones(2,1) * sum(ab,0) ) % (ones(2,1)*wght) * Nrep -
mydigamma(ab) % (ones(2,1)*wght) *Nrep;
for (unsigned int i=0;i<K;i++){
J(0,i) += dx_a(i,i) - dn_ab(i,i);
J(1,i) += dy_b(i,i) - dn_ab(i,i);
}
// compute the trigamma for hessian
// repeatedly use dn_ab, dx_a, dy_b; H_d represents the diagnal; H_o off diagnal of H
dn_ab = cmpTgm(n_ab,K).t() * Postprob;
dx_a = cmpTgm(x_a,K) .t() * Postprob;
dy_b = cmpTgm(y_b,K) .t() * Postprob;
H_d = mytrigamma( ones(2,1) * sum(ab,0) ) % (ones(2,1)*wght) * Nrep -
mytrigamma(ab) % (ones(2,1)*wght) *Nrep;
for (unsigned int i=0;i<K;i++){
H_d(0,i) += dx_a(i,i) - dn_ab(i,i); //
H_d(1,i) += dy_b(i,i) - dn_ab(i,i);
}
H_o = ( mytrigamma( ones(2,1) * sum(ab,0) ) % (ones(2,1)*wght) * Nrep ) - ones(2,1) * dn_ab.diag().t();
H = diagmat(vectorise(H_d));
for(unsigned int i=0;i<K;i++){
H(2*i,1+2*i) = H_o(1,i);
H(1+2*i,2*i) = H_o(1,i);
}
// likelihood computation
px = Nrep*mylgamma(ones(N,1)*sum(ab,0)) - Nrep*mylgamma(ones(N,1)*ab.row(0)) - Nrep*mylgamma(ones(N,1)*ab.row(1))
- cmpLgm(n_ab,K) + cmpLgm(x_a,K) + cmpLgm(y_b,K);
g = -t * vectorise(J) - F.t() * D * ones(m,1); // g first dierivatives of the function
H = -t * H; // H Hessian
for (unsigned int i=0;i<m;i++){
d(i) = log(-d(i));
}
f = -t * accu(px % Postprob) - sum(d); // f value for output function
return {g,H,f};
}
//' Matrix left-multiplied by its transpose
//'
//' Given matrix A, the procedure returns A'A.
//'
//' @param x Numeric matrix.
// [[Rcpp::export]]
arma::mat tmult(arma::mat x) {
return(x.t()*x);
}
//[[Rcpp::export]]
List cmpHmm(const arma::mat x, arma::mat y, arma::mat trans, arma::mat ab, arma::mat F, arma::vec h){
unsigned int Nrep = x.n_cols;
unsigned int K = ab.n_cols;
unsigned int N = x.n_rows;
unsigned int Nit = 30;
double t_step;
double mu = 1e6;
double PRECISION = 1e8;
double t_INITIAL = 1;
double ALPHA = 0.1;
double BETA = 0.7;
double NTTOL = 1e-6;
double s;
double lambda;
List out(4);
CVXOBJ cvx;
CVXOBJ cvx_new;
arma::mat n = x + y;
arma::mat Dens(N,K);
arma::mat Forward(N,K);
arma::mat Backward(N,K);
arma::mat Postprob(N,K);
arma::rowvec wght(K);
arma::vec Scale(N);
Backward.row(N-1).fill(0);
Scale(0) = 1.0;
arma::vec logl;
logl.zeros(Nit+1);
arma::vec v(2*K); // inverse(H)*J
for(unsigned int nit=0;nit<Nit;nit++){
Dens = exp( Nrep*mylgamma(ones(N,1)*sum(ab,0)) - Nrep*mylgamma(ones(N,1)*ab.row(0)) - Nrep*mylgamma(ones(N,1)*ab.row(1))
- cmpLgm(N_ab(n,sum(ab,0)),K) + cmpLgm(N_ab(x,ab.row(0)),K) + cmpLgm(N_ab(y,ab.row(1)),K)
+ mylgamma(n+1.0) * ones(Nrep,K) - mylgamma(x+1.0) * ones(Nrep,K) - mylgamma(y+1.0) * ones(Nrep,K)
);
Forward.row(0) = Dens.row(0)/K;
for (unsigned int n=1;n<N;n++){
Forward.row(n) = ( Forward.row(n-1) * trans ) % Dens.row(n);
Scale(n) = sum(Forward.row(n));
Forward.row(n) = Forward.row(n) / Scale(n);
}
logl(nit+1) = log(sum(Forward.row(N-1))) + sum(logvec(Scale,N)); // caculate the likelhood remember end at N-1
Backward.row(N-1) += 1;
for (int n=N-2;n>=0;n--){
Backward.row(n) = ( Backward.row(n+1) % Dens.row(n+1) ) * trans.t();
Backward.row(n) = Backward.row(n) / Scale(n);
}
trans = trans % ( Forward.rows(0,N-2).t() * ( Dens.rows(1,N-1) % Backward.rows(1,N-1) ) );
trans = trans / ( sum(trans,1) * ones(1,K) );
Postprob = Forward % Backward;
Postprob = Postprob / ( sum(Postprob,1) * ones(1,K) );
wght = sum(Postprob,0);
t_step = t_INITIAL;
while (t_step < PRECISION ){
// for (unsigned int i=0;i<2;i++){
cvx = cvxObj(t_step,Postprob,wght,x,y,n,ab,F,h,N,Nrep);
v = -solve( cvx.H,cvx.g );
lambda = sum(v % cvx.g);
s = 1;
while(min(h - F * (vectorise(ab) + s*v)) < 0) {
s = BETA*s;
}
cvx_new = cvxObj(t_step,Postprob,wght,x,y,n,ab_sv(ab,s,v,K),F,h,N,Nrep);
while (cvx_new.f > cvx.f + ALPHA*s*lambda) {
s = BETA * s;
cvx_new = cvxObj(t_step,Postprob,wght,x,y,n,ab_sv(ab,s,v,K),F,h,N,Nrep);
}
if (std::abs(lambda/2) < NTTOL) {break;}
ab = ab_sv(ab,s,v,K);
t_step = mu * t_step;
}
if (std::abs( (logl(nit+1) - logl(nit)) / logl(nit+1) ) < NTTOL) {break;}
}
out[0] = ab;
out[1] = trans;
out[2] = Postprob;
out[3] = logl;
return out;
}
