tensor_predictors/tensorPredictors/R/TSIR.R

103 lines
3.4 KiB
R

#' Tensor Sliced Inverse Regression
#'
#' @export
TSIR <- function(X, y, d, sample.axis = 1L,
max.iter = 50L,
eps = sqrt(.Machine$double.eps)
) {
if (!(is.factor(y) || is.integer(y))) { # TODO: Implement continuous case!
stop("Only factor and integer response implemented!")
}
stopifnot(exprs = {
dim(X)[sample.axis] == length(y)
length(d) + 1L == length(dim(X))
})
# rearrange `X`, `Fy` such that the last axis enumerates observations
axis.perm <- c(seq_along(dim(X))[-sample.axis], sample.axis)
X <- aperm(X, axis.perm)
# get dimensions
n <- tail(dim(X), 1)
p <- head(dim(X), -1)
modes <- seq_along(p)
# reinterpretation of `y` as factor index as number of different slices
y <- as.factor(y)
nr.slices <- length(levels(y))
slice.sizes <- table(y)
y <- as.integer(y)
# center `X`
X <- X - c(rowMeans(X, dim = length(modes)))
# Slice `X` into slices governed by `y`
slices <- Map(function(s) {
X_s <- X[rep(s == y, each = prod(p))]
dim(X_s) <- c(p, slice.sizes[s])
X_s
}, seq_len(nr.slices))
# For each slice we get the slice means
slice.means <- Map(rowMeans, slices, MoreArgs = list(dim = length(modes)))
# Initial `Gamma_k` estimates as dominent eigenvalues of `Cov_c(E[X_(k) | Y])`
Sigmas <- Map(function(k) {
Reduce(`+`, Map(function(X_s, mu_s, n_s) {
mcrossprod(rowMeans(X_s - c(mu_s), dims = length(modes)), mode = k)
}, slices, slice.means, slice.sizes)) / nr.slices
}, modes)
Gammas <- Map(`[[`, Map(La.svd, Sigmas, nu = d, nv = 0), list("u"))
# setup projections as `Proj_k = Gamma_k Gamma_k'`
projections <- Map(tcrossprod, Gammas)
# compute initial loss for the break condition
loss.last <- n^-1 * Reduce(`+`, Map(function(X_s, n_s) {
n_s * sum((X_s - mlm(X_s, projections))^2)
}, slice.means, slice.sizes))
# Iterate till convergence
for (iter in seq_len(max.iter)) {
# For each mode assume mode reduction `Gamma`s fixed and update
# current mode reduction `Gamma_k`
for (k in modes) {
# Other mode projection of slice means
slice.proj <- Map(mlm, slice.means, MoreArgs = list(
Gammas[-k], modes[-k], transposed = TRUE
))
# Update mode `k` slice mean covariances
Sigmas[[k]] <- n^-1 * Reduce(`+`, Map(function(PX_s, n_s) {
n_s * mcrossprod(PX_s, mode = k)
}, slice.proj, slice.sizes))
# Recompute mode `k` basis `Gamma_k`
Gammas[[k]] <- La.svd(Sigmas[[k]], nu = d[k], nv = 0)$u
# update mode `k` projection matrix onto the new span of `Gamma_k`
projections[[k]] <- tcrossprod(Gammas[[k]])
# compute loss for break condition
loss <- n^-1 * Reduce(`+`, Map(function(X_s, n_s) {
n_s * sum((X_s - mlm(X_s, projections))^2)
}, slice.means, slice.sizes))
}
# check break condition
if (abs(loss - loss.last) < eps * loss) {
break
}
loss.last <- loss
}
# mode sample covariance matrices
Omegas <- Map(function(k) n^-1 * mcrossprod(X, mode = k), modes)
# reductions matrices `Omega_k^-1 Gamma_k` where there (reverse) kronecker
# product spans the central tensor subspace (CTS) estimate
Map(solve, Omegas, Gammas)
}