added Ising sims
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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_2b_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 <- 0x2bL, "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(2, 3) # predictor `X` dimension
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dimF <- c(2, 2) # "function" `F(y)` of responce `y` dimension
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betas <- Map(diag, 1, dimX, dimF)
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Omegas <- list(toeplitz(c(0, -2)), toeplitz(seq(1, 0, by = -0.5)))
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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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# 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 <- 23
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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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)["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, 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), 1),
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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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@ -0,0 +1,195 @@
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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_2c_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 <- 0x2cL, "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(2, 3) # predictor `X` dimension
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dimF <- c(2, 2) # "function" `F(y)` of responce `y` dimension
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betas <- list(
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`[<-`(matrix(0, dimX[1], dimF[1]), 1, , c(1, 1)),
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`[<-`(matrix(0, dimX[2], dimF[2]), 2, , c(1, -1))
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)
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Omegas <- list(toeplitz(c(0, -2)), toeplitz(seq(1, 0, by = -0.5)))
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# compute true (full) model parameters to compair estimates against
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B.true <- as.matrix(as.numeric((1:6) == 3))
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# define projections onto rank 1 matrices for betas
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proj.betas <- Map(.projRank, rep(1L, length(betas)))
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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 <- 26
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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"), # < 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.betas = proj.betas)
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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. = 1L)
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)["user.self"]
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time.hopca <- system.time(
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fit.hopca <- HOPCA(X, npc = c(1L, 1L), 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 = 1L,
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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 = 1L,
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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 = c(1L, 1L), 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(1L, 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 <- qr.Q(qr(with(fit.gmlm, Reduce(`%x%`, rev(betas)))))[, 1L, drop = FALSE]
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B.tnormal <- qr.Q(qr(with(attr(fit.gmlm, "tensor_normal"), Reduce(`%x%`, rev(betas)))))[, 1L, drop = FALSE]
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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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# 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",
|
||||
xlab = "Sample Size", ylab = "Time [s]",
|
||||
ylim = c(0, max(sim[startsWith(names(sim), "time")])))
|
||||
|
|
@ -0,0 +1,213 @@
|
|||
library(tensorPredictors)
|
||||
library(logisticPCA)
|
||||
# library(RGCCA)
|
||||
# Use modified version of `RGCCA`
|
||||
# Reasons (on Ubuntu 22.04 LTS):
|
||||
# - compatible with `Rscript`
|
||||
# - about 4 times faster for small problems
|
||||
# Changes:
|
||||
# - Run in main thread, avoid `parallel::makeCluster` if `n_cores == 1`
|
||||
# (file "R/mgccak.R" lines 81:103)
|
||||
# - added `Encoding: UTF-8`
|
||||
# (file "DESCRIPTION")
|
||||
suppressWarnings({
|
||||
devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)
|
||||
})
|
||||
|
||||
setwd("~/Work/tensorPredictors/sim/")
|
||||
base.name <- format(Sys.time(), "sim_2d_ising-%Y%m%dT%H%M")
|
||||
|
||||
# Source utility function used in most simulations (extracted for convenience)
|
||||
source("./sim_utils.R")
|
||||
|
||||
# Set PRNG seed for reproducability
|
||||
# Note: `0x` is the HEX number prefix and the trailing `L` stands for "long"
|
||||
# which is `R`s way if indicating an integer.
|
||||
set.seed(seed <- 0x2dL, "Mersenne-Twister", "Inversion", "Rejection")
|
||||
|
||||
|
||||
reps <- 100 # number of simulation replications
|
||||
sample.sizes <- c(100, 200, 300, 500, 750) # sample sizes `n`
|
||||
dimX <- c(2, 3) # predictor `X` dimension
|
||||
dimF <- c(2, 2) # "function" `F(y)` of responce `y` dimension
|
||||
|
||||
betas <- Map(diag, 1, dimX, dimF)
|
||||
# # All identical couplings with log odds of 1, that is approx
|
||||
# # `P(X_i = 1, X_j = 1 | X_-i,-j = 0) ~ 3 / 4`
|
||||
# Omegas <- Map(function(dim) `diag<-`(matrix(1, dim, dim), 0), dimX)
|
||||
Omegas <- list(
|
||||
`diag<-`(matrix(0.5, dimX[1], dimX[1]), 0),
|
||||
diag(dimX[2])
|
||||
)
|
||||
|
||||
# compute true (full) model parameters to compair estimates against
|
||||
B.true <- Reduce(`%x%`, rev(betas))
|
||||
|
||||
# Build projections onto `all elements are equal except diagonal is zero` matrices
|
||||
# proj.Omegas <- Map(function(Omega) {
|
||||
# proj <- as.vector(Omega) %*% pinv(as.vector(Omega))
|
||||
# function(Omega) {
|
||||
# matrix(proj %*% as.vector(Omega), nrow = nrow(Omega))
|
||||
# }
|
||||
# }, Omegas)
|
||||
proj.Omegas <- Map(.projMaskedMean, Map(as.logical, Omegas))
|
||||
|
||||
# data sampling routine
|
||||
sample.data <- function(sample.size, betas, Omegas) {
|
||||
dimX <- mapply(nrow, betas)
|
||||
dimF <- mapply(ncol, betas)
|
||||
|
||||
# generate response (sample axis is last axis)
|
||||
y <- runif(sample.size, -1, 1)
|
||||
F <- aperm(array(c(
|
||||
sinpi(y), -cospi(y),
|
||||
cospi(y), sinpi(y)
|
||||
), dim = c(length(y), 2, 2)), c(2, 3, 1))
|
||||
|
||||
Omega <- Reduce(kronecker, rev(Omegas))
|
||||
|
||||
X <- apply(F, 3, function(Fi) {
|
||||
dim(Fi) <- dimF
|
||||
params <- diag(as.vector(mlm(Fi, betas))) + Omega
|
||||
tensorPredictors::ising_sample(1, params)
|
||||
})
|
||||
dim(X) <- c(dimX, sample.size)
|
||||
|
||||
list(X = X, F = F, y = y, sample.axis = 3)
|
||||
}
|
||||
|
||||
# # has been run once with initial seed
|
||||
# lpca.hyper.param <- local({
|
||||
# c(X, F, y, sample.axis) %<-% sample.data(1e3, betas, Omegas)
|
||||
# vecX <- mat(X, sample.axis)
|
||||
# CV <- cv.lpca(vecX, ks = prod(dimF), ms = seq(1, 30, by = 1))
|
||||
# # plot(CV)
|
||||
# as.numeric(colnames(CV))[which.min(CV)]
|
||||
# })
|
||||
# set.seed(seed, "Mersenne-Twister", "Inversion", "Rejection")
|
||||
lpca.hyper.param <- 10
|
||||
|
||||
|
||||
# Create a CSV logger to write simulation results to
|
||||
log.file <- paste(base.name, "csv", sep = ".")
|
||||
logger <- CSV.logger(
|
||||
file.name = log.file,
|
||||
header = c("sample.size", "rep", outer(
|
||||
c("time", "dist.subspace", "dist.projection"), # < measures, v methods
|
||||
c("gmlm", "tnormal", "pca", "hopca", "lpca", "clpca", "tsir", "mgcca"),
|
||||
paste, sep = "."
|
||||
))
|
||||
)
|
||||
|
||||
|
||||
### for each sample size
|
||||
for (sample.size in sample.sizes) {
|
||||
# repeate every simulation
|
||||
for (rep in seq_len(reps)) {
|
||||
# Sample training data
|
||||
c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
|
||||
|
||||
# start timing for reporting
|
||||
start.timer()
|
||||
|
||||
# fit different models
|
||||
# Wrapped in try-catch clock to ensure the simulation continues,
|
||||
# if an error occures continue with nest resplication and log an error message
|
||||
try.catch.block <- tryCatch({
|
||||
time.gmlm <- system.time(
|
||||
fit.gmlm <- gmlm_ising(X, F, y, sample.axis = sample.axis,
|
||||
proj.Omegas = proj.Omegas)
|
||||
)["user.self"]
|
||||
time.tnormal <- -1 # part of Ising gmlm (not relevent here)
|
||||
time.pca <- system.time(
|
||||
fit.pca <- prcomp(mat(X, sample.axis), rank. = prod(dimF))
|
||||
)["user.self"]
|
||||
time.hopca <- system.time(
|
||||
fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
|
||||
)["user.self"]
|
||||
time.lpca <- system.time(
|
||||
fit.lpca <- logisticPCA(mat(X, sample.axis), k = prod(dimF),
|
||||
m = lpca.hyper.param)
|
||||
)["user.self"]
|
||||
time.clpca <- system.time(
|
||||
fit.clpca <- convexLogisticPCA(mat(X, sample.axis), k = prod(dimF),
|
||||
m = lpca.hyper.param)
|
||||
)["user.self"]
|
||||
time.tsir <- system.time(
|
||||
fit.tsir <- TSIR(X, y, d = dimF, sample.axis = sample.axis)
|
||||
)["user.self"]
|
||||
# `mgcca` expects the first axis to be the sample axis
|
||||
X1 <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
|
||||
F1 <- cbind(sinpi(y), cospi(y))
|
||||
time.mgcca <- system.time(
|
||||
fit.mgcca <- mgcca(list(X1, F1), ncomp = c(prod(dimF), 1L),
|
||||
quiet = TRUE, scheme = "factorial")
|
||||
)["user.self"]
|
||||
}, error = print)
|
||||
|
||||
# Get elapsed time from last timer start and the accumulated total time
|
||||
# (_not_ a precide timing, only to get an idea)
|
||||
c(elapsed, total.time) %<-% end.timer()
|
||||
|
||||
# Drop comparison in case any error (in any fitting routine)
|
||||
if (inherits(try.catch.block, "error")) { next }
|
||||
|
||||
# Compute true reduction matrix
|
||||
B.gmlm <- with(fit.gmlm, Reduce(`%x%`, rev(betas)))
|
||||
B.tnormal <- with(attr(fit.gmlm, "tensor_normal"), Reduce(`%x%`, rev(betas)))
|
||||
B.pca <- fit.pca$rotation
|
||||
B.hopca <- Reduce(`%x%`, rev(fit.hopca))
|
||||
B.lpca <- fit.lpca$U
|
||||
B.clpca <- fit.clpca$U
|
||||
B.tsir <- Reduce(`%x%`, rev(fit.tsir))
|
||||
B.mgcca <- fit.mgcca$astar[[1]]
|
||||
|
||||
# Subspace Distances: Normalized `|| P_A - P_B ||_F` where
|
||||
# `P_A = A (A' A)^-1 A'` and the normalization means that with
|
||||
# respect to the dimensions of `A, B` the subspace distance is in the
|
||||
# range `[0, 1]`.
|
||||
dist.subspace.gmlm <- dist.subspace(B.true, B.gmlm, normalize = TRUE)
|
||||
dist.subspace.tnormal <- dist.subspace(B.true, B.tnormal, normalize = TRUE)
|
||||
dist.subspace.pca <- dist.subspace(B.true, B.pca, normalize = TRUE)
|
||||
dist.subspace.hopca <- dist.subspace(B.true, B.hopca, normalize = TRUE)
|
||||
dist.subspace.lpca <- dist.subspace(B.true, B.lpca, normalize = TRUE)
|
||||
dist.subspace.clpca <- dist.subspace(B.true, B.clpca, normalize = TRUE)
|
||||
dist.subspace.tsir <- dist.subspace(B.true, B.tsir, normalize = TRUE)
|
||||
dist.subspace.mgcca <- dist.subspace(B.true, B.mgcca, normalize = TRUE)
|
||||
|
||||
# Projection Distances: Spectral norm (2-norm) `|| P_A - P_B ||_2`.
|
||||
dist.projection.gmlm <- dist.projection(B.true, B.gmlm)
|
||||
dist.projection.tnormal <- dist.projection(B.true, B.tnormal)
|
||||
dist.projection.pca <- dist.projection(B.true, B.pca)
|
||||
dist.projection.hopca <- dist.projection(B.true, B.hopca)
|
||||
dist.projection.lpca <- dist.projection(B.true, B.lpca)
|
||||
dist.projection.clpca <- dist.projection(B.true, B.clpca)
|
||||
dist.projection.tsir <- dist.projection(B.true, B.tsir)
|
||||
dist.projection.mgcca <- dist.projection(B.true, B.mgcca)
|
||||
|
||||
# Call CSV logger writing results to file
|
||||
logger()
|
||||
|
||||
# print progress
|
||||
cat(sprintf("sample size (%d): %d/%d - rep: %d/%d - elapsed: %.1f [s], total: %.0f [s]\n",
|
||||
sample.size, which(sample.size == sample.sizes),
|
||||
length(sample.sizes), rep, reps, elapsed, total.time))
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
### read simulation results generate plots
|
||||
if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }
|
||||
|
||||
sim <- read.csv(log.file)
|
||||
|
||||
|
||||
plot.sim(sim, "dist.subspace", main = "Subspace Distance",
|
||||
xlab = "Sample Size", ylab = "Distance")
|
||||
|
||||
# plot.sim(sim, "dist.projection", main = "Projection Distance",
|
||||
# xlab = "Sample Size", ylab = "Distance")
|
||||
|
||||
plot.sim(sim, "time", main = "Runtime",
|
||||
xlab = "Sample Size", ylab = "Time [s]",
|
||||
ylim = c(0, max(sim[startsWith(names(sim), "time")])))
|
||||
|
|
@ -0,0 +1,244 @@
|
|||
library(tensorPredictors)
|
||||
# library(logisticPCA)
|
||||
# # library(RGCCA)
|
||||
# # Use modified version of `RGCCA`
|
||||
# # Reasons (on Ubuntu 22.04 LTS):
|
||||
# # - compatible with `Rscript`
|
||||
# # - about 4 times faster for small problems
|
||||
# # Changes:
|
||||
# # - Run in main thread, avoid `parallel::makeCluster` if `n_cores == 1`
|
||||
# # (file "R/mgccak.R" lines 81:103)
|
||||
# # - added `Encoding: UTF-8`
|
||||
# # (file "DESCRIPTION")
|
||||
# suppressWarnings({
|
||||
# devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)
|
||||
# })
|
||||
|
||||
# setwd("~/Work/tensorPredictors/sim/")
|
||||
# base.name <- format(Sys.time(), "sim_2e_ising-%Y%m%dT%H%M")
|
||||
|
||||
# # Source utility function used in most simulations (extracted for convenience)
|
||||
# source("./sim_utils.R")
|
||||
|
||||
# # Set PRNG seed for reproducability
|
||||
# # Note: `0x` is the HEX number prefix and the trailing `L` stands for "long"
|
||||
# # which is `R`s way if indicating an integer.
|
||||
# set.seed(seed <- 0x2eL, "Mersenne-Twister", "Inversion", "Rejection")
|
||||
|
||||
|
||||
reps <- 100 # number of simulation replications
|
||||
sample.sizes <- c(100, 200, 300, 500, 750) # sample sizes `n`
|
||||
dimX <- c(5, 5, 5) # predictor `X` dimension
|
||||
dimF <- c(2, 2, 2) # "function" `F(y)` of responce `y` dimension
|
||||
|
||||
betas <- Map(matrix, 1, dimX, dimF)
|
||||
|
||||
Omegas <- Map(function(p) `diag<-`(matrix(0.5, p, p), 0), dimX)
|
||||
|
||||
|
||||
# data sampling routine
|
||||
sample.data <- function(sample.size, betas, Omegas) {
|
||||
dimX <- mapply(nrow, betas)
|
||||
dimF <- mapply(ncol, betas)
|
||||
|
||||
# generate response (sample axis is last axis)
|
||||
y <- runif(sample.size, -1, 1)
|
||||
F <- aperm(array(c(
|
||||
+sinpi(y), +sinpi(2 * y),
|
||||
+cospi(y), +cospi(2 * y),
|
||||
-cospi(y), -cospi(2 * y),
|
||||
+sinpi(y), +sinpi(2 * y)
|
||||
), dim = c(length(y), 2, 2, 2)), c(2, 3, 4, 1))
|
||||
|
||||
Omega <- Reduce(kronecker, rev(Omegas))
|
||||
|
||||
X <- apply(F, length(dim(F)), function(Fi) {
|
||||
dim(Fi) <- dimF
|
||||
params <- diag(as.vector(mlm(Fi, betas))) + Omega
|
||||
tensorPredictors::ising_sample(1, params)
|
||||
})
|
||||
dim(X) <- c(dimX, sample.size)
|
||||
|
||||
list(X = X, F = F, y = y, sample.axis = 3)
|
||||
}
|
||||
|
||||
sample.size <- 100L
|
||||
|
||||
# Sample training data
|
||||
c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
# compute true (full) model parameters to compair estimates against
|
||||
B.true <- Reduce(`%x%`, rev(betas))
|
||||
|
||||
# Build projections onto `all elements are equal except diagonal is zero` matrices
|
||||
# proj.Omegas <- Map(function(Omega) {
|
||||
# proj <- as.vector(Omega) %*% pinv(as.vector(Omega))
|
||||
# function(Omega) {
|
||||
# matrix(proj %*% as.vector(Omega), nrow = nrow(Omega))
|
||||
# }
|
||||
# }, Omegas)
|
||||
proj.Omegas <- Map(.projMaskedMean, Map(as.logical, Omegas))
|
||||
|
||||
# data sampling routine
|
||||
sample.data <- function(sample.size, betas, Omegas) {
|
||||
dimX <- mapply(nrow, betas)
|
||||
dimF <- mapply(ncol, betas)
|
||||
|
||||
# generate response (sample axis is last axis)
|
||||
y <- runif(sample.size, -1, 1)
|
||||
F <- aperm(array(c(
|
||||
sinpi(y), -cospi(y),
|
||||
cospi(y), sinpi(y)
|
||||
), dim = c(length(y), 2, 2)), c(2, 3, 1))
|
||||
|
||||
Omega <- Reduce(kronecker, rev(Omegas))
|
||||
|
||||
X <- apply(F, 3, function(Fi) {
|
||||
dim(Fi) <- dimF
|
||||
params <- diag(as.vector(mlm(Fi, betas))) + Omega
|
||||
tensorPredictors::ising_sample(1, params)
|
||||
})
|
||||
dim(X) <- c(dimX, sample.size)
|
||||
|
||||
list(X = X, F = F, y = y, sample.axis = 3)
|
||||
}
|
||||
|
||||
# # has been run once with initial seed
|
||||
# lpca.hyper.param <- local({
|
||||
# c(X, F, y, sample.axis) %<-% sample.data(1e3, betas, Omegas)
|
||||
# vecX <- mat(X, sample.axis)
|
||||
# CV <- cv.lpca(vecX, ks = prod(dimF), ms = seq(1, 30, by = 1))
|
||||
# # plot(CV)
|
||||
# as.numeric(colnames(CV))[which.min(CV)]
|
||||
# })
|
||||
# set.seed(seed, "Mersenne-Twister", "Inversion", "Rejection")
|
||||
lpca.hyper.param <- 10
|
||||
|
||||
|
||||
# Create a CSV logger to write simulation results to
|
||||
log.file <- paste(base.name, "csv", sep = ".")
|
||||
logger <- CSV.logger(
|
||||
file.name = log.file,
|
||||
header = c("sample.size", "rep", outer(
|
||||
c("time", "dist.subspace", "dist.projection"), # < measures, v methods
|
||||
c("gmlm", "tnormal", "pca", "hopca", "lpca", "clpca", "tsir", "mgcca"),
|
||||
paste, sep = "."
|
||||
))
|
||||
)
|
||||
|
||||
|
||||
### for each sample size
|
||||
for (sample.size in sample.sizes) {
|
||||
# repeate every simulation
|
||||
for (rep in seq_len(reps)) {
|
||||
# Sample training data
|
||||
c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
|
||||
|
||||
# start timing for reporting
|
||||
start.timer()
|
||||
|
||||
# fit different models
|
||||
# Wrapped in try-catch clock to ensure the simulation continues,
|
||||
# if an error occures continue with nest resplication and log an error message
|
||||
try.catch.block <- tryCatch({
|
||||
time.gmlm <- system.time(
|
||||
fit.gmlm <- gmlm_ising(X, F, y, sample.axis = sample.axis,
|
||||
proj.Omegas = proj.Omegas)
|
||||
)["user.self"]
|
||||
time.tnormal <- -1 # part of Ising gmlm (not relevent here)
|
||||
time.pca <- system.time(
|
||||
fit.pca <- prcomp(mat(X, sample.axis), rank. = prod(dimF))
|
||||
)["user.self"]
|
||||
time.hopca <- system.time(
|
||||
fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
|
||||
)["user.self"]
|
||||
time.lpca <- system.time(
|
||||
fit.lpca <- logisticPCA(mat(X, sample.axis), k = prod(dimF),
|
||||
m = lpca.hyper.param)
|
||||
)["user.self"]
|
||||
time.clpca <- system.time(
|
||||
fit.clpca <- convexLogisticPCA(mat(X, sample.axis), k = prod(dimF),
|
||||
m = lpca.hyper.param)
|
||||
)["user.self"]
|
||||
time.tsir <- system.time(
|
||||
fit.tsir <- TSIR(X, y, d = dimF, sample.axis = sample.axis)
|
||||
)["user.self"]
|
||||
# `mgcca` expects the first axis to be the sample axis
|
||||
X1 <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
|
||||
F1 <- cbind(sinpi(y), cospi(y))
|
||||
time.mgcca <- system.time(
|
||||
fit.mgcca <- mgcca(list(X1, F1), ncomp = c(prod(dimF), 1L),
|
||||
quiet = TRUE, scheme = "factorial")
|
||||
)["user.self"]
|
||||
}, error = print)
|
||||
|
||||
# Get elapsed time from last timer start and the accumulated total time
|
||||
# (_not_ a precide timing, only to get an idea)
|
||||
c(elapsed, total.time) %<-% end.timer()
|
||||
|
||||
# Drop comparison in case any error (in any fitting routine)
|
||||
if (inherits(try.catch.block, "error")) { next }
|
||||
|
||||
# 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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|
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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
|
||||
# respect to the dimensions of `A, B` the subspace distance is in the
|
||||
# range `[0, 1]`.
|
||||
dist.subspace.gmlm <- dist.subspace(B.true, B.gmlm, normalize = TRUE)
|
||||
dist.subspace.tnormal <- dist.subspace(B.true, B.tnormal, normalize = TRUE)
|
||||
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)
|
||||
dist.subspace.lpca <- dist.subspace(B.true, B.lpca, normalize = TRUE)
|
||||
dist.subspace.clpca <- dist.subspace(B.true, B.clpca, normalize = TRUE)
|
||||
dist.subspace.tsir <- dist.subspace(B.true, B.tsir, normalize = TRUE)
|
||||
dist.subspace.mgcca <- dist.subspace(B.true, B.mgcca, normalize = TRUE)
|
||||
|
||||
# Projection Distances: Spectral norm (2-norm) `|| P_A - P_B ||_2`.
|
||||
dist.projection.gmlm <- dist.projection(B.true, B.gmlm)
|
||||
dist.projection.tnormal <- dist.projection(B.true, B.tnormal)
|
||||
dist.projection.pca <- dist.projection(B.true, B.pca)
|
||||
dist.projection.hopca <- dist.projection(B.true, B.hopca)
|
||||
dist.projection.lpca <- dist.projection(B.true, B.lpca)
|
||||
dist.projection.clpca <- dist.projection(B.true, B.clpca)
|
||||
dist.projection.tsir <- dist.projection(B.true, B.tsir)
|
||||
dist.projection.mgcca <- dist.projection(B.true, B.mgcca)
|
||||
|
||||
# Call CSV logger writing results to file
|
||||
logger()
|
||||
|
||||
# print progress
|
||||
cat(sprintf("sample size (%d): %d/%d - rep: %d/%d - elapsed: %.1f [s], total: %.0f [s]\n",
|
||||
sample.size, which(sample.size == sample.sizes),
|
||||
length(sample.sizes), rep, reps, elapsed, total.time))
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
### read simulation results generate plots
|
||||
if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }
|
||||
|
||||
sim <- read.csv(log.file)
|
||||
|
||||
|
||||
plot.sim(sim, "dist.subspace", main = "Subspace Distance",
|
||||
xlab = "Sample Size", ylab = "Distance")
|
||||
|
||||
# plot.sim(sim, "dist.projection", main = "Projection Distance",
|
||||
# xlab = "Sample Size", ylab = "Distance")
|
||||
|
||||
plot.sim(sim, "time", main = "Runtime",
|
||||
xlab = "Sample Size", ylab = "Time [s]",
|
||||
ylim = c(0, max(sim[startsWith(names(sim), "time")])))
|
||||
Loading…
Reference in New Issue