245 lines
9.1 KiB
R
245 lines
9.1 KiB
R
library(tensorPredictors)
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# library(logisticPCA)
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# # library(RGCCA)
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# # Use modified version of `RGCCA`
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# # Reasons (on Ubuntu 22.04 LTS):
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# # - compatible with `Rscript`
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# # - about 4 times faster for small problems
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# # Changes:
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# # - Run in main thread, avoid `parallel::makeCluster` if `n_cores == 1`
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# # (file "R/mgccak.R" lines 81:103)
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# # - added `Encoding: UTF-8`
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# # (file "DESCRIPTION")
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# suppressWarnings({
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# devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)
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# })
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# setwd("~/Work/tensorPredictors/sim/")
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# base.name <- format(Sys.time(), "sim_2e_ising-%Y%m%dT%H%M")
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# # Source utility function used in most simulations (extracted for convenience)
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# source("./sim_utils.R")
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# # Set PRNG seed for reproducability
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# # Note: `0x` is the HEX number prefix and the trailing `L` stands for "long"
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# # which is `R`s way if indicating an integer.
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# set.seed(seed <- 0x2eL, "Mersenne-Twister", "Inversion", "Rejection")
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reps <- 100 # number of simulation replications
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sample.sizes <- c(100, 200, 300, 500, 750) # sample sizes `n`
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dimX <- c(5, 5, 5) # predictor `X` dimension
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dimF <- c(2, 2, 2) # "function" `F(y)` of responce `y` dimension
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betas <- Map(matrix, 1, dimX, dimF)
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Omegas <- Map(function(p) `diag<-`(matrix(0.5, p, p), 0), dimX)
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# data sampling routine
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sample.data <- function(sample.size, betas, Omegas) {
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dimX <- mapply(nrow, betas)
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dimF <- mapply(ncol, betas)
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# generate response (sample axis is last axis)
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y <- runif(sample.size, -1, 1)
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F <- aperm(array(c(
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+sinpi(y), +sinpi(2 * y),
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+cospi(y), +cospi(2 * y),
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-cospi(y), -cospi(2 * y),
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+sinpi(y), +sinpi(2 * y)
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), dim = c(length(y), 2, 2, 2)), c(2, 3, 4, 1))
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Omega <- Reduce(kronecker, rev(Omegas))
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X <- apply(F, length(dim(F)), function(Fi) {
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dim(Fi) <- dimF
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params <- diag(as.vector(mlm(Fi, betas))) + Omega
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tensorPredictors::ising_sample(1, params)
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})
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dim(X) <- c(dimX, sample.size)
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list(X = X, F = F, y = y, sample.axis = 3)
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}
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sample.size <- 100L
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# Sample training data
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c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
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# compute true (full) model parameters to compair estimates against
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B.true <- Reduce(`%x%`, rev(betas))
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# Build projections onto `all elements are equal except diagonal is zero` matrices
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# proj.Omegas <- Map(function(Omega) {
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# proj <- as.vector(Omega) %*% pinv(as.vector(Omega))
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# function(Omega) {
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# matrix(proj %*% as.vector(Omega), nrow = nrow(Omega))
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# }
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# }, Omegas)
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proj.Omegas <- Map(.projMaskedMean, Map(as.logical, Omegas))
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# data sampling routine
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sample.data <- function(sample.size, betas, Omegas) {
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dimX <- mapply(nrow, betas)
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dimF <- mapply(ncol, betas)
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# generate response (sample axis is last axis)
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y <- runif(sample.size, -1, 1)
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F <- aperm(array(c(
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sinpi(y), -cospi(y),
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cospi(y), sinpi(y)
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), dim = c(length(y), 2, 2)), c(2, 3, 1))
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Omega <- Reduce(kronecker, rev(Omegas))
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X <- apply(F, 3, function(Fi) {
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dim(Fi) <- dimF
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params <- diag(as.vector(mlm(Fi, betas))) + Omega
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tensorPredictors::ising_sample(1, params)
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})
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dim(X) <- c(dimX, sample.size)
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list(X = X, F = F, y = y, sample.axis = 3)
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}
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# # has been run once with initial seed
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# lpca.hyper.param <- local({
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# c(X, F, y, sample.axis) %<-% sample.data(1e3, betas, Omegas)
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# vecX <- mat(X, sample.axis)
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# CV <- cv.lpca(vecX, ks = prod(dimF), ms = seq(1, 30, by = 1))
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# # plot(CV)
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# as.numeric(colnames(CV))[which.min(CV)]
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# })
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# set.seed(seed, "Mersenne-Twister", "Inversion", "Rejection")
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lpca.hyper.param <- 10
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# Create a CSV logger to write simulation results to
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log.file <- paste(base.name, "csv", sep = ".")
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logger <- CSV.logger(
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file.name = log.file,
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header = c("sample.size", "rep", outer(
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c("time", "dist.subspace", "dist.projection"), # < measures, v methods
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c("gmlm", "tnormal", "pca", "hopca", "lpca", "clpca", "tsir", "mgcca"),
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paste, sep = "."
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))
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)
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### for each sample size
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for (sample.size in sample.sizes) {
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# repeate every simulation
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for (rep in seq_len(reps)) {
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# Sample training data
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c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
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# start timing for reporting
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start.timer()
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# fit different models
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# Wrapped in try-catch clock to ensure the simulation continues,
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# if an error occures continue with nest resplication and log an error message
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try.catch.block <- tryCatch({
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time.gmlm <- system.time(
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fit.gmlm <- gmlm_ising(X, F, y, sample.axis = sample.axis,
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proj.Omegas = proj.Omegas)
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)["user.self"]
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time.tnormal <- -1 # part of Ising gmlm (not relevent here)
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time.pca <- system.time(
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fit.pca <- prcomp(mat(X, sample.axis), rank. = prod(dimF))
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)["user.self"]
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time.hopca <- system.time(
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fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
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)["user.self"]
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time.lpca <- system.time(
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fit.lpca <- logisticPCA(mat(X, sample.axis), k = prod(dimF),
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m = lpca.hyper.param)
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)["user.self"]
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time.clpca <- system.time(
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fit.clpca <- convexLogisticPCA(mat(X, sample.axis), k = prod(dimF),
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m = lpca.hyper.param)
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)["user.self"]
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time.tsir <- system.time(
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fit.tsir <- TSIR(X, y, d = dimF, sample.axis = sample.axis)
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)["user.self"]
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# `mgcca` expects the first axis to be the sample axis
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X1 <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
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F1 <- cbind(sinpi(y), cospi(y))
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time.mgcca <- system.time(
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fit.mgcca <- mgcca(list(X1, F1), ncomp = c(prod(dimF), 1L),
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quiet = TRUE, scheme = "factorial")
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)["user.self"]
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}, error = print)
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# Get elapsed time from last timer start and the accumulated total time
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# (_not_ a precide timing, only to get an idea)
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c(elapsed, total.time) %<-% end.timer()
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# Drop comparison in case any error (in any fitting routine)
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if (inherits(try.catch.block, "error")) { next }
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# Compute true reduction matrix
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B.gmlm <- with(fit.gmlm, Reduce(`%x%`, rev(betas)))
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B.tnormal <- with(attr(fit.gmlm, "tensor_normal"), Reduce(`%x%`, rev(betas)))
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B.pca <- fit.pca$rotation
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B.hopca <- Reduce(`%x%`, rev(fit.hopca))
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B.lpca <- fit.lpca$U
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B.clpca <- fit.clpca$U
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B.tsir <- Reduce(`%x%`, rev(fit.tsir))
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B.mgcca <- fit.mgcca$astar[[1]]
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# Subspace Distances: Normalized `|| P_A - P_B ||_F` where
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# `P_A = A (A' A)^-1 A'` and the normalization means that with
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# respect to the dimensions of `A, B` the subspace distance is in the
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# range `[0, 1]`.
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dist.subspace.gmlm <- dist.subspace(B.true, B.gmlm, normalize = TRUE)
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dist.subspace.tnormal <- dist.subspace(B.true, B.tnormal, normalize = TRUE)
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dist.subspace.pca <- dist.subspace(B.true, B.pca, normalize = TRUE)
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dist.subspace.hopca <- dist.subspace(B.true, B.hopca, normalize = TRUE)
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dist.subspace.lpca <- dist.subspace(B.true, B.lpca, normalize = TRUE)
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dist.subspace.clpca <- dist.subspace(B.true, B.clpca, normalize = TRUE)
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dist.subspace.tsir <- dist.subspace(B.true, B.tsir, normalize = TRUE)
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dist.subspace.mgcca <- dist.subspace(B.true, B.mgcca, normalize = TRUE)
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# Projection Distances: Spectral norm (2-norm) `|| P_A - P_B ||_2`.
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dist.projection.gmlm <- dist.projection(B.true, B.gmlm)
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dist.projection.tnormal <- dist.projection(B.true, B.tnormal)
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dist.projection.pca <- dist.projection(B.true, B.pca)
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dist.projection.hopca <- dist.projection(B.true, B.hopca)
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dist.projection.lpca <- dist.projection(B.true, B.lpca)
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dist.projection.clpca <- dist.projection(B.true, B.clpca)
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dist.projection.tsir <- dist.projection(B.true, B.tsir)
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dist.projection.mgcca <- dist.projection(B.true, B.mgcca)
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# Call CSV logger writing results to file
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logger()
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# print progress
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cat(sprintf("sample size (%d): %d/%d - rep: %d/%d - elapsed: %.1f [s], total: %.0f [s]\n",
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sample.size, which(sample.size == sample.sizes),
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length(sample.sizes), rep, reps, elapsed, total.time))
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}
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}
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### read simulation results generate plots
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if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }
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sim <- read.csv(log.file)
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plot.sim(sim, "dist.subspace", main = "Subspace Distance",
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xlab = "Sample Size", ylab = "Distance")
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# plot.sim(sim, "dist.projection", main = "Projection Distance",
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# xlab = "Sample Size", ylab = "Distance")
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plot.sim(sim, "time", main = "Runtime",
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xlab = "Sample Size", ylab = "Time [s]",
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ylim = c(0, max(sim[startsWith(names(sim), "time")])))
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