#' constructionModelesLassoMLE #' #' Construct a collection of models with the Lasso-MLE procedure. #' #' @param phiInit an initialization for phi, get by initSmallEM.R #' @param rhoInit an initialization for rho, get by initSmallEM.R #' @param piInit an initialization for pi, get by initSmallEM.R #' @param gamInit an initialization for gam, get by initSmallEM.R #' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10 #' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100 #' @param gamma integer for the power in the penaly, by default = 1 #' @param X matrix of covariates (of size n*p) #' @param Y matrix of responses (of size n*m) #' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4 #' @param S output of selectVariables.R #' @param ncores Number of cores, by default = 3 #' @param fast TRUE to use compiled C code, FALSE for R code only #' @param verbose TRUE to show some execution traces #' #' @return a list with several models, defined by phi, rho, pi, llh #' #' @export constructionModelesLassoMLE <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, X, Y, eps, S, ncores = 3, fast, verbose) { if (ncores > 1) { cl <- parallel::makeCluster(ncores, outfile = "") parallel::clusterExport(cl, envir = environment(), varlist = c("phiInit", "rhoInit", "gamInit", "mini", "maxi", "gamma", "X", "Y", "eps", "S", "ncores", "fast", "verbose")) } # Individual model computation computeAtLambda <- function(lambda) { if (ncores > 1) require("valse") #nodes start with an empty environment if (verbose) print(paste("Computations for lambda=", lambda)) n <- nrow(X) p <- ncol(X) m <- ncol(Y) k <- length(piInit) sel.lambda <- S[[lambda]]$selected # col.sel = which(colSums(sel.lambda)!=0) #if boolean matrix col.sel <- which(sapply(sel.lambda, length) > 0) #if list of selected vars if (length(col.sel) == 0) return(NULL) # lambda == 0 because we compute the EMV: no penalization here res <- EMGLLF(array(phiInit,dim=c(p,m,k))[col.sel, , ], rhoInit, piInit, gamInit, mini, maxi, gamma, 0, as.matrix(X[, col.sel]), Y, eps, fast) # Eval dimension from the result + selected phiLambda2 <- res$phi rhoLambda <- res$rho piLambda <- res$pi phiLambda <- array(0, dim = c(p, m, k)) for (j in seq_along(col.sel)) phiLambda[col.sel[j], sel.lambda[[j]], ] <- phiLambda2[j, sel.lambda[[j]], ] dimension <- length(unlist(sel.lambda)) ## Affectations Gam <- matrix(0, ncol = length(piLambda), nrow = n) for (i in 1:n) { for (r in 1:length(piLambda)) { sqNorm2 <- sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2) Gam[i, r] <- piLambda[r] * exp(-0.5 * sqNorm2) * det(rhoLambda[, , r]) } } Gam2 <- Gam/rowSums(Gam) affec <- apply(Gam2, 1, which.max) proba <- Gam2 LLH <- c(sum(log(apply(Gam,1,sum))), (dimension + m + 1) * k - 1) # ## Computation of the loglikelihood # # Precompute det(rhoLambda[,,r]) for r in 1...k # detRho <- sapply(1:k, function(r) gdet(rhoLambda[, , r])) # sumLogLLH <- 0 # for (i in 1:n) # { # # Update gam[,]; use log to avoid numerical problems # logGam <- sapply(1:k, function(r) { # log(piLambda[r]) + log(detRho[r]) - 0.5 * # sum((Y[i, ] %*% rhoLambda[, , r] - X[i, ] %*% phiLambda[, , r])^2) # }) # # #logGam <- logGam - max(logGam) #adjust without changing proportions -> change the LLH # gam <- exp(logGam) # norm_fact <- sum(gam) # sumLogLLH <- sumLogLLH + log(norm_fact) - m/2* log(2 * base::pi) # } #llhLambda <- c(-sumLogLLH/n, (dimension + m + 1) * k - 1) list(phi = phiLambda, rho = rhoLambda, pi = piLambda, llh = LLH, affec = affec, proba = proba) } # For each lambda, computation of the parameters out <- if (ncores > 1) { parLapply(cl, 1:length(S), computeAtLambda) } else { lapply(1:length(S), computeAtLambda) } if (ncores > 1) parallel::stopCluster(cl) out }