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#' Update the second mode in a CP model.
#'
#' Update is performed in place to avoid memory issues. There is no return value.
#'
#' @export
#' @param m A \code{CP_model} object created with \code{mk_model}
#' @param d Input data object created with \code{input_data}
#' @param params List of parameters created with \code{get_model_params()}
#' @examples
#' data.params <- get_data_params(c('decomp=CP'))
#' toy <- mk_toy(data.params)
#' train.data <- input_data$new(mode1.X=toy$mode1.X[,-1],
#' mode2.X=toy$mode2.X[,-1],
#' mode3.X=toy$mode3.X,
#' resp=toy$resp)
#' model.params <- get_model_params(c('decomp=CP'))
#' toy.model <- mk_model(train.data, model.params)
#' toy.model$rand_init(model.params)
#'
#' update_mode2_CP(m=toy.model, d=train.data, params=model.params)
update_mode2_CP <- function(m, d, params) {
J <- dim(d$resp)[2]
Q <- nrow(m$mode2.A.mean)
R <- ncol(m$mode2.H.mean)
# If the intercept term is removed change A1.intercept
A2.intercept <- ifelse('const' %in% rownames(m$mode2.A.mean), T, F)
if(Q != 0) { # If there is no input data, skip updates for lambda and A
if(params$verbose) print("Updating prior lambda vector for mode 2")
m2.A.var <- matrix(0, Q, R)
for(r in 1:R) m2.A.var[,r] <- diagonal(m$mode2.A.cov[,,r])
if(params$row.share) {
m$mode2.lambda.scale <- 1/(.5*(rowSums(m$mode2.A.mean^2 + m2.A.var)) + 1/m$m2.beta)
} else m$mode2.lambda.scale <- 1/(.5*(m$mode2.A.mean^2 + m2.A.var) + 1/m$m2.beta)
if(params$verbose) print("Updating projection (A) matrix for mode 2")
# Update mode2.A covariance parameters. They only rely on X and lambdas
lambda.exp <- m$mode2.lambda.shape * m$mode2.lambda.scale
for(r in 1:R) {
if(params$row.share) {
m$mode2.A.cov[,,r] <- chol2inv(chol(diagonal(lambda.exp) + (1/m$m2.sigma2) * m$m2Xm2X))
} else
m$mode2.A.cov[,,r] <- chol2inv(chol(diagonal(lambda.exp[,r]) + (1/m$m2.sigma2) * m$m2Xm2X))
}
# Update A means
if(A2.intercept) {
for(r in 1:R) m$mode2.A.mean[,r] <- (1/m$m2.sigma2) *
(m$mode2.A.cov[,,r] %*% t(cbind(1,d$mode2.X)) %*% m$mode2.H.mean[,r])
} else {
for(r in 1:R) m$mode2.A.mean[,r] <- (1/m$m2.sigma2) *
(m$mode2.A.cov[,,r] %*% t(d$mode2.X) %*% m$mode2.H.mean[,r])
}
}
if(params$verbose) print("Updating latent (H) matrix for mode 2")
# Update the variance first. sapply vectorizes the updates for each row
for(r in 1:R) {
m$mode2.H.var[,r] <- sapply(1:J, function(j) 1/((1/m$sigma2) *
sum(d$delta[,j,] * outer((m$mode1.H.mean[,r]^2 + m$mode1.H.var[,r]),
(m$mode3.H.mean[,r]^2 + m$mode3.H.var[,r]))) + 1/m$m2.sigma2))
}
# Next update the mean
for(j in 1:J) {
for(r in 1:R) {
if(Q == 0) {x_times_a <- 0} else {
x_times_a <- safe_prod(d$mode2.X[j,,drop=F], m$mode2.A.mean[,r,drop=F])
}
m$mode2.H.mean[j,r] <- m$mode2.H.var[j,r] * ((1/m$sigma2) *
sum(outer(m$mode1.H.mean[,r], m$mode3.H.mean[,r]) *
(d$resp[,j,] - (sweep(m$mode1.H.mean[,-r,drop=F], MARGIN=2, m$mode2.H.mean[j,-r], '*') %*%
t(m$mode3.H.mean[,-r,drop=F]))), na.rm=T) + 1/m$m2.sigma2 * x_times_a)
}
}
}
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