# This file is part of the `locus` R package:
# https://github.com/hruffieux/locus
#
# Internal core function to call the variational algorithm for identity link,
# fixed covariates and no external annotation variables.
# See help of `locus` function for details.
#
locus_z_core_ <- function(Y, X, Z, list_hyper, gam_vb, alpha_vb, mu_beta_vb,
sig2_alpha_vb, sig2_beta_vb, tau_vb, tol, maxit, anneal,
verbose, batch = "y", full_output = FALSE, debug = TRUE) {
# Y must have been centered, and X and Z, standardized (except the intercept in Z).
d <- ncol(Y)
n <- nrow(Y)
p <- ncol(X)
q <- ncol(Z)
# Preparing annealing if any
#
if (is.null(anneal)) {
annealing <- FALSE
c <- 1
} else {
annealing <- TRUE
ladder <- get_annealing_ladder_(anneal, verbose)
c <- ladder[1]
}
eps <- .Machine$double.eps^0.5
with(list_hyper, { # list_init not used with the with() function to avoid
# copy-on-write for large objects
m2_alpha <- update_m2_alpha_(alpha_vb, sig2_alpha_vb)
beta_vb <- update_beta_vb_(gam_vb, mu_beta_vb)
m2_beta <- update_m2_beta_(gam_vb, mu_beta_vb, sig2_beta_vb, sweep = TRUE)
mat_x_m1 <- update_mat_x_m1_(X, beta_vb)
mat_z_mu <- update_mat_z_mu_(Z, alpha_vb)
rs_gam <- rowSums(gam_vb)
sum_gam <- sum(rs_gam)
converged <- FALSE
lb_new <- -Inf
it <- 0
while ((!converged) & (it < maxit)) {
lb_old <- lb_new
it <- it + 1
if (verbose & (it == 1 | it %% 5 == 0))
cat(paste0("Iteration ", format(it), "... \n"))
digam_sum <- digamma(c * (a + b + d) - 2 * c + 2)
# % #
phi_vb <- update_phi_z_vb_(phi, d, c = c)
xi_vb <- update_xi_z_vb_(xi, tau_vb, m2_alpha, c = c) ###
zeta2_inv_vb <- phi_vb / xi_vb
# % #
# % #
lambda_vb <- update_lambda_vb_(lambda, sum_gam, c = c)
nu_vb <- update_nu_vb_(nu, m2_beta, tau_vb, c = c)
sig2_inv_vb <- lambda_vb / nu_vb
# % #
# % #
eta_vb <- update_eta_z_vb_(n, q, eta, gam_vb, c = c)
kappa_vb <- update_kappa_z_vb_(Y, Z, kappa, alpha_vb, beta_vb,
m2_alpha, m2_beta, mat_x_m1, mat_z_mu,
sig2_inv_vb, zeta2_inv_vb, c = c)
tau_vb <- eta_vb / kappa_vb
# % #
sig2_alpha_vb <- update_sig2_alpha_vb_(n, zeta2_inv_vb, tau_vb, c = c)
sig2_beta_vb <- update_sig2_beta_vb_(n, sig2_inv_vb, tau_vb, c = c)
log_tau_vb <- update_log_tau_vb_(eta_vb, kappa_vb)
log_sig2_inv_vb <- update_log_sig2_inv_vb_(lambda_vb, nu_vb)
# different possible batch-coordinate ascent schemes:
if (batch == "y") { # optimal scheme
log_om_vb <- update_log_om_vb(a, digam_sum, rs_gam, c = c)
log_1_min_om_vb <- update_log_1_min_om_vb(b, d, digam_sum, rs_gam, c = c)
for (i in sample(1:q)) {
mat_z_mu <- mat_z_mu - tcrossprod(Z[, i], alpha_vb[i, ])
alpha_vb[i, ] <- c * sig2_alpha_vb[i, ] * (tau_vb *
crossprod(Y - mat_z_mu - mat_x_m1, Z[, i]))
mat_z_mu <- mat_z_mu + tcrossprod(Z[, i], alpha_vb[i, ])
}
# C++ Eigen call for expensive updates
shuffled_ind <- as.numeric(sample(0:(p-1))) # Zero-based index in C++
coreZLoop(X, Y, gam_vb, log_om_vb, log_1_min_om_vb, log_sig2_inv_vb,
log_tau_vb, beta_vb, mat_x_m1, mat_z_mu, mu_beta_vb,
sig2_beta_vb, tau_vb, shuffled_ind, c = c)
rs_gam <- rowSums(gam_vb)
} else if (batch == "x") { # used only internally, convergence not ensured
log_om_vb <- update_log_om_vb(a, digam_sum, rs_gam, c = c)
log_1_min_om_vb <- update_log_1_min_om_vb(b, d, digam_sum, rs_gam, c = c)
for (k in sample(1:d)) {
alpha_vb[, k] <- c * sig2_alpha_vb[, k] * tau_vb[k] *
(crossprod(Y[, k] - mat_z_mu[, k] - mat_x_m1[, k], Z) + (n - 1) * alpha_vb[, k])
mat_z_mu[, k] <- Z %*% alpha_vb[, k]
mu_beta_vb[, k] <- c * sig2_beta_vb[k] * tau_vb[k] *
(crossprod(Y[, k] - mat_z_mu[, k] - mat_x_m1[, k], X) + (n - 1) * beta_vb[, k])
gam_vb[, k] <- exp(-log_one_plus_exp_(c * (log_1_min_om_vb - log_om_vb -
log_tau_vb[k] / 2 - log_sig2_inv_vb / 2 -
mu_beta_vb[, k] ^ 2 / (2 * sig2_beta_vb[k]) -
log(sig2_beta_vb[k]) / 2)))
beta_vb[, k] <- mu_beta_vb[, k] * gam_vb[, k]
mat_x_m1[, k] <- X %*% beta_vb[, k]
}
rs_gam <- rowSums(gam_vb)
} else if (batch == "x-y") { # used only internally, convergence not ensured
if (annealing)
stop("Annealing not implemented for this scheme. Exit.")
log_om_vb <- update_log_om_vb(a, digam_sum, rs_gam, c = c)
log_1_min_om_vb <- update_log_1_min_om_vb(b, d, digam_sum, rs_gam, c = c)
alpha_vb <- sweep(sig2_alpha_vb * (crossprod(Z, Y - mat_z_mu - mat_x_m1) + (n - 1) * alpha_vb), 2, tau_vb, `*`)
mat_z_mu <- Z %*% alpha_vb
# C++ Eigen call for expensive updates
coreZBatch(X, Y, gam_vb, log_om_vb, log_1_min_om_vb, log_sig2_inv_vb,
log_tau_vb, beta_vb, mat_x_m1, mat_z_mu, mu_beta_vb, sig2_beta_vb, tau_vb)
rs_gam <- rowSums(gam_vb)
} else if (batch == "0"){ # no batch, used only internally
for (k in sample(1:d)) {
log_om_vb <- update_log_om_vb(a, digam_sum, rs_gam, c = c)
log_1_min_om_vb <- update_log_1_min_om_vb(b, d, digam_sum, rs_gam, c = c)
for (i in sample(1:q)) {
mat_z_mu[, k] <- mat_z_mu[, k] - Z[, i] * alpha_vb[i, k]
alpha_vb[i, k] <- c * sig2_alpha_vb[i, k] * tau_vb[k] *
crossprod(Z[, i], Y[,k] - mat_z_mu[, k] - mat_x_m1[, k])
mat_z_mu[, k] <- mat_z_mu[, k] + Z[, i] * alpha_vb[i, k]
}
for (j in sample(1:p)) {
mat_x_m1[, k] <- mat_x_m1[, k] - X[, j] * beta_vb[j, k]
mu_beta_vb[j, k] <- c * sig2_beta_vb[k] * tau_vb[k] *
crossprod(Y[,k] - mat_x_m1[, k] - mat_z_mu[, k], X[, j])
gam_vb[j, k] <- exp(-log_one_plus_exp_(c * (log_1_min_om_vb[j] - log_om_vb[j] -
log_tau_vb[k] / 2 - log_sig2_inv_vb / 2 -
mu_beta_vb[j, k] ^ 2 / (2 * sig2_beta_vb[k]) -
log(sig2_beta_vb[k]) / 2)))
beta_vb[j, k] <- mu_beta_vb[j, k] * gam_vb[j, k]
mat_x_m1[, k] <- mat_x_m1[, k] + X[, j] * beta_vb[j, k]
}
rs_gam <- rowSums(gam_vb)
}
} else {
stop ("Batch scheme not defined. Exit.")
}
m2_alpha <- update_m2_alpha_(alpha_vb, sig2_alpha_vb)
m2_beta <- update_m2_beta_(gam_vb, mu_beta_vb, sig2_beta_vb, sweep = TRUE)
a_vb <- update_a_vb(a, rs_gam, c = c)
b_vb <- update_b_vb(b, d, rs_gam, c = c)
om_vb <- a_vb / (a_vb + b_vb)
sum_gam <- sum(rs_gam)
if (annealing) {
if (verbose & (it == 1 | it %% 5 == 0))
cat(paste0("Temperature = ", format(1 / c, digits = 4), "\n\n"))
c <- ifelse(it < length(ladder), ladder[it + 1], 1)
if (isTRUE(all.equal(c, 1))) {
annealing <- FALSE
if (verbose)
cat("** Exiting annealing mode. **\n\n")
}
} else {
lb_new <- elbo_z_(Y, Z, a, a_vb, b, b_vb, beta_vb, eta, gam_vb, kappa, lambda,
alpha_vb, nu, phi, phi_vb, sig2_alpha_vb,
sig2_beta_vb, sig2_inv_vb, tau_vb, xi, zeta2_inv_vb,
m2_alpha, m2_beta, mat_x_m1, mat_z_mu, sum_gam)
if (verbose & (it == 1 | it %% 5 == 0))
cat(paste0("ELBO = ", format(lb_new), "\n\n"))
if (debug && lb_new + eps < lb_old)
stop("ELBO not increasing monotonically. Exit. ")
converged <- (abs(lb_new - lb_old) < tol)
}
}
if (verbose) {
if (converged) {
cat(paste0("Convergence obtained after ", format(it), " iterations. \n",
"Optimal marginal log-likelihood variational lower bound ",
"(ELBO) = ", format(lb_new), ". \n\n"))
} else {
warning("Maximal number of iterations reached before convergence. Exit.")
}
}
lb_opt <- lb_new
names_x <- colnames(X)
names_y <- colnames(Y)
names_z <- colnames(Z)
rownames(gam_vb) <- rownames(beta_vb) <- names_x
colnames(gam_vb) <- colnames(beta_vb) <- names_y
names(om_vb) <- names_x
rownames(alpha_vb) <- names_z
colnames(alpha_vb) <- names_y
diff_lb <- abs(lb_opt - lb_old)
if (full_output) { # for internal use only
create_named_list_(a, a_vb, b, b_vb, beta_vb, eta, gam_vb, kappa, lambda,
alpha_vb, mu_beta_vb, nu, om_vb, phi, phi_vb,
sig2_alpha_vb, sig2_beta_vb, sig2_inv_vb, tau_vb, xi,
zeta2_inv_vb, m2_alpha, m2_beta, sum_gam, converged,
it, lb_opt, diff_lb, annealing)
} else {
create_named_list_(beta_vb, gam_vb, om_vb, alpha_vb, converged, it, lb_opt, diff_lb, annealing)
}
})
}
# Internal function which implements the marginal log-likelihood variational
# lower bound (ELBO) corresponding to the `locus_z_core` algorithm.
#
elbo_z_ <- function(Y, Z, a, a_vb, b, b_vb, beta_vb, eta, gam_vb, kappa, lambda,
alpha_vb, nu, phi, phi_vb, sig2_alpha_vb, sig2_beta_vb,
sig2_inv_vb, tau_vb, xi, zeta2_inv_vb, m2_alpha, m2_beta,
mat_x_m1, mat_z_mu, sum_gam) {
n <- nrow(Y)
q <- ncol(Z)
xi_vb <- update_xi_z_vb_(xi, tau_vb, m2_alpha)
eta_vb <- update_eta_z_vb_(n, q, eta, gam_vb)
kappa_vb <- update_kappa_z_vb_(Y, Z, kappa, alpha_vb, beta_vb, m2_alpha,
m2_beta, mat_x_m1, mat_z_mu, sig2_inv_vb,
zeta2_inv_vb)
lambda_vb <- update_lambda_vb_(lambda, sum_gam)
nu_vb <- update_nu_vb_(nu, m2_beta, tau_vb)
log_tau_vb <- digamma(eta_vb) - log(kappa_vb)
log_zeta2_inv_vb <- digamma(phi_vb) - log(xi_vb)
log_sig2_inv_vb <- digamma(lambda_vb) - log(nu_vb)
log_om_vb <- digamma(a_vb) - digamma(a_vb + b_vb)
log_1_min_om_vb <- digamma(b_vb) - digamma(a_vb + b_vb)
elbo_A <- e_y_(n, kappa, kappa_vb, log_tau_vb, m2_beta, sig2_inv_vb, tau_vb,
m2_alpha, zeta2_inv_vb)
elbo_B <- e_beta_gamma_(gam_vb, log_om_vb, log_1_min_om_vb, log_sig2_inv_vb,
log_tau_vb, m2_beta, sig2_beta_vb, sig2_inv_vb, tau_vb)
elbo_C <- e_tau_(eta, eta_vb, kappa, kappa_vb, log_tau_vb, tau_vb)
elbo_D <- e_sig2_inv_(lambda, lambda_vb, log_sig2_inv_vb, nu, nu_vb, sig2_inv_vb)
elbo_E <- e_omega_(a, a_vb, b, b_vb, log_om_vb, log_1_min_om_vb)
elbo_F <- e_alpha_(m2_alpha, log_tau_vb, log_zeta2_inv_vb, sig2_alpha_vb,
tau_vb, zeta2_inv_vb)
elbo_G <- e_zeta2_inv_(log_zeta2_inv_vb, phi, phi_vb, xi, xi_vb, zeta2_inv_vb)
elbo_A + elbo_B + elbo_C + elbo_D + elbo_E + elbo_F + elbo_G
}
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