tensor_predictors/tensorPredictors/R/kpir_base.R

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#' (Slightly altered) old implementation
#'
#' @export
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kpir.base <- function(X, Fy, shape = c(dim(X)[-1], dim(Fy[-1])),
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method = c("mle", "ls"),
eps1 = 1e-10, eps2 = 1e-10, max.iter = 500L,
logger = NULL
) {
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# Check if X and Fy have same number of observations
stopifnot(nrow(X) == NROW(Fy))
n <- nrow(X) # Number of observations
# Get and check predictor dimensions
if (length(dim(X)) == 2L) {
stopifnot(!missing(shape))
stopifnot(ncol(X) == prod(shape[1:2]))
p <- as.integer(shape[1]) # Predictor "height"
q <- as.integer(shape[2]) # Predictor "width"
} else if (length(dim(X)) == 3L) {
p <- dim(X)[2]
q <- dim(X)[3]
dim(X) <- c(n, p * q)
} else {
stop("'X' must be a matrix or 3-tensor")
}
# Get and check response dimensions
if (!is.array(Fy)) {
Fy <- as.array(Fy)
}
if (length(dim(Fy)) == 1L) {
k <- r <- 1L
dim(Fy) <- c(n, 1L)
} else if (length(dim(Fy)) == 2L) {
stopifnot(!missing(shape))
stopifnot(ncol(Fy) == prod(shape[3:4]))
k <- as.integer(shape[3]) # Response functional "height"
r <- as.integer(shape[4]) # Response functional "width"
} else if (length(dim(Fy)) == 3L) {
k <- dim(Fy)[2]
r <- dim(Fy)[3]
dim(Fy) <- c(n, k * r)
} else {
stop("'Fy' must be a vector, matrix or 3-tensor")
}
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log.likelihood <- function(par, X, Fy, Delta.inv, da, db) {
alpha <- matrix(par[1:prod(da)], da[1L])
beta <- matrix(par[(prod(da) + 1):length(par)], db[1L])
error <- X - tcrossprod(Fy, kronecker(alpha, beta))
sum(error * (error %*% Delta.inv))
}
# Validate method using unexact matching.
method <- match.arg(method)
### Step 1: (Approx) Least Squares solution for `X = Fy B' + epsilon`
cpFy <- crossprod(Fy)
if (n <= k * r || qr(cpFy)$rank < k * r) {
# In case of under-determined system replace the inverse in the normal
# equation by the Moore-Penrose Pseudo Inverse
B <- t(matpow(cpFy, -1) %*% crossprod(Fy, X))
} else {
# Compute OLS estimate by the Normal Equation
B <- t(solve(cpFy, crossprod(Fy, X)))
}
# Estimate alpha, beta as nearest kronecker approximation.
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c(alpha, beta) %<-% approx.kronecker(B, c(q, r), c(p, k))
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if (method == "ls") {
# Estimate Delta.
B <- kronecker(alpha, beta)
rank <- if (ncol(Fy) == 1) 1L else qr(Fy)$rank
resid <- X - tcrossprod(Fy, B)
Delta <- crossprod(resid) / (nrow(X) - rank)
} else { # mle
B <- kronecker(alpha, beta)
# Compute residuals
resid <- X - tcrossprod(Fy, B)
# Estimate initial Delta.
Delta <- crossprod(resid) / nrow(X)
# call logger with initial starting value
if (is.function(logger)) {
# Transformed Residuals (using `matpow` as robust inversion algo,
# uses Moore-Penrose Pseudo Inverse in case of singular `Delta`)
resid.trans <- resid %*% matpow(Delta, -1)
loss <- 0.5 * (nrow(X) * log(det(Delta)) + sum(resid.trans * resid))
logger(0L, loss, alpha, beta, Delta, NA)
}
for (iter in 1:max.iter) {
# Optimize log-likelihood for alpha, beta with fixed Delta.
opt <- optim(c(alpha, beta), log.likelihood, gr = NULL,
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X, Fy, matpow(Delta, -1), c(q, r), c(p, k))
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# Store previous alpha, beta and Delta (for break consition).
Delta.last <- Delta
B.last <- B
# Extract optimized alpha, beta.
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alpha <- matrix(opt$par[1:(q * r)], q, r)
beta <- matrix(opt$par[(q * r + 1):length(opt$par)], p, k)
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# Calc new Delta with likelihood optimized alpha, beta.
B <- kronecker(alpha, beta)
resid <- X - tcrossprod(Fy, B)
Delta <- crossprod(resid) / nrow(X)
# call logger before break condition check
if (is.function(logger)) {
# Transformed Residuals (using `matpow` as robust inversion algo,
# uses Moore-Penrose Pseudo Inverse in case of singular `Delta`)
resid.trans <- resid %*% matpow(Delta, -1)
loss <- 0.5 * (nrow(X) * log(det(Delta)) + sum(resid.trans * resid))
logger(iter, loss, alpha, beta, Delta, NA)
}
# Check break condition 1.
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if (norm(Delta - Delta.last, "F") < eps1 * norm(Delta, "F")) {
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# Check break condition 2.
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if (norm(B - B.last, "F") < eps2 * norm(B, "F")) {
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break
}
}
}
}
# calc final loss
resid.trans <- resid %*% matpow(Delta, -1)
loss <- 0.5 * (nrow(X) * log(det(Delta)) + sum(resid.trans * resid))
list(loss = loss, alpha = alpha, beta = beta, Delta = Delta)
}