316 lines
11 KiB
R
316 lines
11 KiB
R
# library(tensorPredictors)
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devtools::load_all("~/Work/tensorPredictors/tensorPredictors", export_all = FALSE)
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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_2a_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(0x2aL, "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 <- rep(1, length(dimX)) # "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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# 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(prod(sample.size, dimF), -2, 2)
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F <- array(y, dim = c(dimF, sample.size)) # ~ U[-1, 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 = length(dim(X)))
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}
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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, 20, by = 0.5))
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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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# 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
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c("gmlm", "tnormal", "pca", "hopca", "lpca", "clpca", "tsir", "mgcca"), # methods
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paste, sep = "."
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))
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)
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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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### 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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# 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, 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), 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), 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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time.mgcca <- system.time(
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fit.mgcca <- mgcca(
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list(X1, y), # `drop` removes 1D axis
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quiet = TRUE,
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scheme = "factorial",
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ncomp = c(1, 1)
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)
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)["user.self"]
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}, error = print)
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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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# equiv to Subspace distance in this case
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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\n",
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sample.size, which(sample.size == sample.sizes),
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length(sample.sizes), rep, reps))
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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]", ylim = c(0, 18))
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# aggr <- aggregate(sim, list(sim$sample.size), sd)
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# stats <- aggr[, c(2, 5, 7, 9, 11, 13, 15, 17, 19)]
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# names(stats) <- Map(tail, strsplit(names(stats), ".", fixed = TRUE), 1)
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# round(stats * 100, 2)
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# sim <- sim[!startsWith(names(sim), "time")]
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# sim <- sim[names(sim) != "rep"]
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# names(sim) <- strsplit(names(stats), ".", fixed = TRUE)
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# (as.data.frame(Map(function(m, s) {
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# paste0(round(m, 2), " (", round(s, 2), ")")
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# },
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# aggregate(sim, list(sim$size), mean),
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# aggregate(sim, list(sim$size), sd)
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# )))
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# $n$ & gmlm & pca & hopca lpca & clpca & tsir & mgcca
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# 100 & 0.34 (0.14) & 0.90 (0.04) & 0.90 (0.05) 0.94 (0.09) & 1 0.91 (0.03) & 0.48 (0.19) & 0.55 (0.13)
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# 200 & 0.25 (0.11) & 0.90 (0.03) & 0.90 (0.03) 0.96 (0.07) & 2 0.91 (0.02) & 0.38 (0.16) & 0.53 (0.10)
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# 300 & 0.20 (0.09) & 0.89 (0.02) & 0.89 (0.02) 0.97 (0.06) & 3 0.91 (0.02) & 0.29 (0.13) & 0.51 (0.11)
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# 500 & 0.16 (0.07) & 0.90 (0.02) & 0.90 (0.02) 0.98 (0.01) & 4 0.91 (0.01) & 0.23 (0.10) & 0.50 (0.08)
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# 750 & 0.13 (0.05) & 0.90 (0.01) & 0.90 (0.01) 0.98 (0.02) & 5 0.91 (0.01) & 0.23 (0.08) & 0.53 (0.06)
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if (FALSE) {
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################################################################################
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### Work In Progress ###
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################################################################################
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library(tensorPredictors)
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dimX <- c(3, 3, 3)
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dimF <- c(1, 1, 1)
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betas <- Map(diag, 1, dimX, dimF)
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Omegas <- rev(list(
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toeplitz(-1 * (seq_len(dimX[1]) == 2L)),
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toeplitz(seq(1, 0, len = dimX[2])),
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diag(dimX[3])
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))
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Omega <- Reduce(kronecker, rev(Omegas))
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layout(matrix(c(
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1, 3, 4,
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2, 3, 5,
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6, 6, 6
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), nrow = 3, byrow = TRUE), heights = c(8, 8, 1))
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`E(X |` <- function(Y) {
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array(diag(ising_m2(diag(as.vector(mlm(array(Y, dimF), betas))) + Omega)), dimX)
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}
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`E(X |`(Y = -2)
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`E(X |`(Y = +2)
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col <- hcl.colors(256, "Blue-Red 3", rev = FALSE)
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matrixImage(`E(X |`(Y = -2), main = "E[X | Y = -2]", zlim = c(0, 1), col = col)
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matrixImage(`E(X |`(Y = -1), main = "E[X | Y = -1]", zlim = c(0, 1), col = col)
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matrixImage(`E(X |`(Y = 0), main = "E[X | Y = 0]", zlim = c(0, 1), col = col)
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matrixImage(`E(X |`(Y = +1), main = "E[X | Y = +1]", zlim = c(0, 1), col = col)
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matrixImage(`E(X |`(Y = +2), main = "E[X | Y = +2]", zlim = c(0, 1), col = col)
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{
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restor.par <- par(mar = c(1.1, 2.1, 0, 2.1))
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plot(0:1, 0:1, type = "n", xlab = "", ylab = "", axes = FALSE)
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rasterImage(as.raster(matrix(col, nrow = 1)), 0, 0, 1, 1)
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mtext("0", side = 2, las = 1, line = -3)
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mtext("1", side = 4, las = 1, line = -3)
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par(restor.par)
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}
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sample.size <- 100
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c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
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# Design matrix containing vectorized X's
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vecX <- mat(X, sample.axis)
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fit.gmlm <- gmlm_ising(X, F)
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fit.pca <- prcomp(mat(X, sample.axis), rank. = prod(dimF))
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fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
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fit.tsir <- TSIR(X, y, dimF, sample.axis = sample.axis)
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fit.mgcca <- local({
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X1 <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
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F1 <- aperm(F, c(sample.axis, seq_along(dim(X))[-sample.axis]))
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mgcca(
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list(X1, drop(F1)), # `drop` removes 1D axis
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quiet = TRUE,
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scheme = "factorial",
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ncomp = rep(prod(dimF), 2)
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)
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})
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fit.lpca <- logisticPCA(vecX, k = prod(dimF), m = m)
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fit.clpca <- convexLogisticPCA(vecX, k = prod(dimF), m = m)
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B.gmlm <- Reduce(kronecker, rev(fit.gmlm$betas))
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B.pca <- fit.pca$rotation
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B.hopca <- Reduce(`%x%`, rev(fit.hopca))
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B.tsir <- Reduce(`%x%`, rev(fit.tsir))
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B.mgcca <- fit.mgcca$astar[[1]]
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B.lpca <- fit.lpca$U
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B.clpca <- fit.clpca$U
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# B.lsvd <- ???
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dist.subspace(B.true, B.gmlm, normalize = TRUE)
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dist.subspace(B.true, B.pca, normalize = TRUE)
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dist.subspace(B.true, B.hopca, normalize = TRUE)
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dist.subspace(B.true, B.tsir, normalize = TRUE)
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dist.subspace(B.true, B.mgcca, normalize = TRUE)
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dist.subspace(B.true, B.lpca, normalize = TRUE)
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dist.subspace(B.true, B.clpca, normalize = TRUE)
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################################################################################
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### End - Work In Progress ###
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################################################################################
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}
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