#' Generic function for performing Gibbs sampling on BPR model
#'
#' \code{bpr_optim} is a generic function which calles the appropriate methods
#' depending on the class of the object \code{x}. Object \code{x} can be either
#' a \code{\link{list}} or a \code{\link{matrix}}.
#'
#' @param x The input object
#' @param ... Additional parameters
#'
#' @seealso \code{\link{bpr_gibbs.list}}, \code{\link{bpr_gibbs.matrix}}
#'
#' @examples
#' data <- bpr_data
#' out_opt <- bpr_gibbs(x = data, is_parallel = FALSE)
#'
#' @export
bpr_gibbs <- function(x, ...){
UseMethod("bpr_gibbs")
}
# Default function for the generic function 'bpr_gibbs'
bpr_gibbs.default <- function(x, ...){
stop("Object x should be either matrix or list!")
}
#' Gibbs sampling for the BPR model using list x
#'
#' \code{bpr_gibbs.list} computes the posterior of the BPR model using auxiliary
#' variable approach. Since we cannot compute the posterior analytically, a
#' Gibbs sampling scheme is used. This method calls
#' \code{\link{bpr_gibbs.matrix}} to process each element of the list.
#'
#' @param x A list of elements of length N, where each element is an L x 3
#' matrix of observations, where 1st column contains the locations. The 2nd
#' and 3rd columns contain the total trials and number of successes at the
#' corresponding locations, repsectively.
#' @param w_mle A matrix of MLE estimates for the regression coefficients for
#' each genomic region of interest.
#' @param is_parallel Logical, indicating if code should be run in parallel.
#' @param no_cores Number of cores to be used, default is max_no_cores - 2.
#' @inheritParams bpr_gibbs.matrix
#'
#' @return A list containing the following elements:
#' \itemize{
#' \item{ \code{W_opt}: An Nx(M+1) matrix with the optimized parameter values.
#' Each row of the matrix corresponds to each element of the list x. The
#' columns are of the same length as the parameter vector w (i.e. number
#' of basis functions).
#' }
#' \item{ \code{Mus}: An N x M matrix with the RBF centers if basis object is
#' \code{\link{rbf.object}}, otherwise NULL.}
#' \item{ \code{basis}: The basis object.
#' }
#' \item{ \code{w}: The initial values of the parameters w.
#' }
#' \item{ \code{x_extrema}: The min and max values of each promoter region.
#' }
#' }
#'
#' @seealso \code{\link{bpr_optim}}, \code{\link{bpr_optim.matrix}}
#'
#' @examples
#' ex_data <- bpr_data
#' basis <- rbf.object(M=3)
#' out_opt <- bpr_gibbs(x = ex_data, is_parallel = FALSE, basis = basis)
#'
#' @export
bpr_gibbs.list <- function(x, w_mle = NULL, basis = NULL, fit_feature = NULL,
cpg_dens_feat = FALSE, w_0_mean = NULL,
w_0_cov = NULL, gibbs_nsim = 20, gibbs_burn_in = 10,
is_parallel = TRUE, no_cores = NULL, ...){
# Check that x is a list object
assertthat::assert_that(is.list(x))
# Extract number of observations
N <- length(x)
assertthat::assert_that(N > 0)
# Perform checks for initial parameter values
out <- .do_checks_bpr_gibbs(w = w_mle, basis = basis)
w_mle <- out$w
basis <- out$basis
# Number of coefficients
M <- basis$M + 1
if (is.vector(w_mle)){
w_mle <- matrix(w_mle, ncol = M, nrow = N, byrow = TRUE)
}
if (is.null(w_0_mean)){
w_0_mean <- rep(0, M)
}else{
if (length(w_0_mean) != M){
w_0_mean <- rep(0, M)
}
}
if (is.null(w_0_cov)){
w_0_cov <- diag(1, M)
}else{
if (NROW(w_0_cov) != M){
w_0_cov <- diag(1, M)
}
}
# Initialize so the CMD check on R passes without NOTES
i <- 0
# If parallel mode is ON
if (is_parallel){
# If number of cores is not given
if (is.null(no_cores)){
no_cores <- parallel::detectCores() - 2
}else{
if (no_cores >= parallel::detectCores()){
no_cores <- parallel::detectCores() - 1
}
}
if (is.na(no_cores)){
no_cores <- 2
}
# Create cluster object
cl <- parallel::makeCluster(no_cores)
doParallel::registerDoParallel(cl)
# Parallel optimization for each element of x, i.e. for each region i.
res <- foreach::"%dopar%"(obj = foreach::foreach(i = 1:N),
ex = {
out_opt <- bpr_gibbs.matrix(x = x[[i]],
w_mle = w_mle[i, ],
basis = basis,
fit_feature = fit_feature,
cpg_dens_feat = cpg_dens_feat,
w_0_mean = w_0_mean,
w_0_cov = w_0_cov,
gibbs_nsim = gibbs_nsim,
gibbs_burn_in = gibbs_burn_in)
})
# Stop parallel execution
parallel::stopCluster(cl)
}else{
# Sequential optimization for each element of x, i.e. for each region i.
res <- foreach::"%do%"(obj = foreach::foreach(i = 1:N),
ex = {
out_opt <- bpr_gibbs.matrix(x = x[[i]],
w_mle = w_mle[i, ],
basis = basis,
fit_feature = fit_feature,
cpg_dens_feat = cpg_dens_feat,
w_0_mean = w_0_mean,
w_0_cov = w_0_cov,
gibbs_nsim = gibbs_nsim,
gibbs_burn_in = gibbs_burn_in)
})
}
# Matrix for storing optimized coefficients
W_opt <- sapply(res, function(x) x$w_opt)
if (is.matrix(W_opt)){
W_opt <- t(W_opt)
}else{
W_opt <- as.matrix(W_opt)
}
colnames(W_opt) <- paste("w", seq(1, NCOL(W_opt)), sep = "")
# Matrix for storing the centers of RBFs if object class is 'rbf'
Mus <- NULL
if (methods::is(basis, "rbf")){
if (is.null(basis$mus)){
Mus <- sapply(lapply(res, function(x) x$basis), function(y) y$mus)
if (is.matrix(Mus)){
Mus <- t(Mus)
}else{
Mus <- as.matrix(Mus)
}
colnames(Mus) <- paste("mu", seq(1, NCOL(Mus)), sep = "")
}
}
# Matrix for storing extrema promoter values
x_extrema <- t(sapply(res, function(x) x$x_extrema))
return(list(W_opt = W_opt,
Mus = Mus,
basis = basis,
w = w_mle,
x_extrema = x_extrema))
}
#' Gibbs sampling for the BPR model using list x
#'
#' \code{bpr_gibbs.matrix} computes the posterior of the BPR model using auxiliary
#' variable approach. Since we cannot compute the posterior analytically, a
#' Gibbs sampling scheme is used.
#'
#' @param x An L x 3 matrix of observations, where 1st column contains the
#' locations. The 2nd and 3rd columns contain the total trials and number of
#' successes at the corresponding locations, repsectively.
#' @param w_mle A vector of parameters (i.e. coefficients of the basis functions)
#' containing the MLE estimates.
#' @param basis A 'basis' object. See \code{\link{polynomial.object}}
#' @param fit_feature Additional feature on how well the profile fits the
#' methylation data.
#' @param cpg_dens_feat Additional feature for the CpG density across the
#' promoter region.
#' @param w_0_mean The prior mean hyperparameter for w
#' @param w_0_cov The prior covariance hyperparameter for w
#' @param gibbs_nsim Optional argument giving the number of simulations of the
#' Gibbs sampler.
#' @param gibbs_burn_in Optional argument giving the burn in period of the
#' Gibbs sampler.
#' @param ... Additional parameters
#'
#' @return A list containing the following elements:
#' \itemize{
#' \item{ \code{w_opt}: Optimized values for the coefficient vector w.
#' The length of the result is the same as the length of the vector w.
#' }
#' \item{ \code{basis}: The basis object.
#' }
#' }
#'
#' @seealso \code{\link{bpr_optim}}, \code{\link{bpr_optim.list}}
#'
#' @examples
#' basis <- polynomial.object(M=2)
#' w <- c(0.1, 0.1, 0.1)
#' w_0_mean <- rep(0, length(w))
#' w_0_cov <- diag(10, length(w))
#' data <- bpr_data[[1]]
#' out_opt <- bpr_gibbs(x = data, w_mle = w, w_0_mean = w_0_mean,
#' w_0_cov = w_0_cov, basis = basis)
#'
#' basis <- polynomial.object(M=0)
#' w <- c(0.1)
#' w_0_mean <- rep(0, length(w))
#' w_0_cov <- diag(10, length(w))
#' data <- bpr_data[[1]]
#' out_opt <- bpr_gibbs(x = data, w_mle = w, w_0_mean = w_0_mean,
#' w_0_cov = w_0_cov, basis = basis)
#'
#' @importFrom stats optim
#' @importFrom truncnorm rtruncnorm
#' @importFrom mvtnorm rmvnorm
#'
#' @export
bpr_gibbs.matrix <- function(x, w_mle = NULL, basis = NULL, fit_feature = NULL,
cpg_dens_feat = FALSE, w_0_mean = NULL,
w_0_cov = NULL, gibbs_nsim = 20,
gibbs_burn_in = 10, ...){
# Vector for storing CpG locations relative to TSS
obs <- as.vector(x[ ,1])
# Create design matrix H
des_mat <- design_matrix(x = basis, obs = obs)
H <- des_mat$H
basis <- des_mat$basis
M <- basis$M + 1
# Total number of reads for each CpG
N_i <- as.vector(x[, 2])
# Corresponding number of methylated reads for each CpG
m_i <- as.vector(x[, 3])
# Sum of total trials for each observation i
J <- sum(N_i)
# Create extended vector y of length (J x 1)
y <- vector(mode = "integer")
for (i in 1:NROW(x)){
y <- c(y, rep(1, m_i[i]), rep(0, N_i[i] - m_i[i]))
}
N1 <- sum(y) # Number of successes
N0 <- J - N1 # Number of failures
# Create extended design matrix Xx of dimension (J x M)
H <- as.matrix(H[rep(1:NROW(H), N_i), ])
# Conjugate prior on the coefficients \w ~ N(w_0_mean, w_0_cov)
if (is.null(w_0_mean)){
w_0_mean <- rep(0, M)
}else{
if (length(w_0_mean) != M){
w_0_mean <- rep(0, M)
}
}
if (is.null(w_0_cov)){
w_0_cov <- diag(1, M)
}else{
if (NROW(w_0_cov) != M){
w_0_cov <- diag(1, M)
}
}
# Initialize regression coefficients
if (is.null(w_mle)){
w_mle <- rep(0, M)
}
# Matrix storing samples of the \w parameter
w_chain <- matrix(0, nrow = gibbs_nsim, ncol = M)
w_chain[1, ] <- w_mle
# ---------------------------------
# Gibbs sampling algorithm
# ---------------------------------
# Compute posterior variance of w
prec_0 <- solve(w_0_cov)
V <- solve(prec_0 + crossprod(H, H))
# Initialize latent variable Z, from truncated normal
z <- rep(0, J)
z[y == 0] <- rtruncnorm(N0, mean = 0, sd = 1, a = -Inf, b = 0)
z[y == 1] <- rtruncnorm(N1, mean = 0, sd = 1, a = 0, b = Inf)
for (t in 2:gibbs_nsim) {
# Compute posterior mean of w
Mu <- V %*% (prec_0 %*% w_0_mean + crossprod(H, z))
# Draw variable \w from its full conditional: \w | z, X
w <- c(rmvnorm(1, Mu, V))
# Update Mean of z
mu_z <- H %*% w
# Draw latent variable z from its full conditional: z | \w, y, X
z[y == 0] <- rtruncnorm(N0, mean = mu_z[y == 0], sd = 1, a = -Inf, b = 0)
z[y == 1] <- rtruncnorm(N1, mean = mu_z[y == 1], sd = 1, a = 0, b = Inf)
# Store the \theta draws
w_chain[t, ] <- w
}
# # Keep summary statistic and get the mean of the Gibbs samples
# if (NCOL(w_chain) == 1){
# w_opt <- mean(w_samples[(ceiling(gibbs_nsim/4)):gibbs_nsim, ])
# }else{
# w_opt <- as.vector(apply(w_samples[(ceiling(gibbs_nsim/4)):gibbs_nsim, ],
# 2, mean))
# }
if (M == 1){
w_opt <- mean(w_chain[-(1:gibbs_burn_in)])
}else{
w_opt <- colMeans(w_chain[-(1:gibbs_burn_in), ])
}
# If we need to add the goodness of fit to the data as feature
if (!is.null(fit_feature)){
if (identical(fit_feature, "NLL")){
fit <- bpr_likelihood(w = w_opt,
H = H,
data = x[ ,2:3],
is_NLL = TRUE)
}else if (identical(fit_feature, "RMSE")){
# Predictions of the target variables
f_pred <- as.vector(pnorm(H %*% w_opt))
f_true <- x[ ,3] / x[ ,2]
fit <- sqrt(mean( (f_pred - f_true) ^ 2) )
}
w_opt <- c(w_opt, fit)
}
# Add as feature the CpG density in the promoter region
if (cpg_dens_feat){
w_opt <- c(w_opt, length(obs))
}
return(list(w_opt = w_opt,
basis = basis,
x_extrema = c(min(obs), max(obs))))
}
# Internal function to make all the appropriate type checks.
.do_checks_bpr_gibbs <- function(w = NULL, basis = NULL){
if (is.null(basis)){
basis <- rbf.object(M = 3)
}
if (is.null(w)){
w <- rep(0.5, basis$M + 1)
}
if (is.matrix(w)){
if (length(w[1,]) != (basis$M + 1) ){
stop("Coefficients vector should be M+1!")
}
}else{
if (length(w) != (basis$M + 1) ){
stop("Coefficients vector should be M+1, M: number of basis functions!")
}
}
return(list(w = w, basis = basis))
}
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