150 lines
6.0 KiB
R
150 lines
6.0 KiB
R
library(tensorPredictors)
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# library(RGCCA)
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### Load modified version which _does not_ create a clusster in case of
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### `n_cores == 1` allowing huge speed improvements! (at least on Ubuntu 22.04 LTS)
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### Moreover, it is compatible with `Rscript`
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### Also added `Encoding: UTF-8` in `DESCRIPTION`
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devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)
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setwd("~/Work/tensorPredictors/sim/")
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base.name <- format(Sys.time(), "sim_1b_normal-%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(0x1bL, "Mersenne-Twister", "Inversion", "Rejection")
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### Simulation configuration
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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, 5) # predictor `X` dimension
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dimF <- rep(2, length(dimX)) # "function" `F(y)` of responce `y` dimension
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# setup true model parameters
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betas <- Map(diag, 1, dimX, dimF)
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Omegas <- Map(function(pj) 0.5^abs(outer(1:pj, 1:pj, `-`)), dimX) # AR(0.5)
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eta1 <- 0
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# data sampling routine
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sample.data <- function(sample.size, eta1, betas, Omegas) {
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# responce is a standard normal variable
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y <- rnorm(sample.size)
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# F(y) is a tensor of monomials
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F <- sapply(y, function(yi) Reduce(outer, Map(`^`, yi, Map(seq, 0, len = dimF))))
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dim(F) <- c(dimF, sample.size)
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# sample predictors from tensor normal X | Y = y (last axis is sample axis)
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sample.axis <- length(betas) + 1L
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Deltas <- Map(solve, Omegas) # normal covariances
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mu_y <- mlm(mlm(F, betas) + as.vector(eta1), Deltas) # conditional mean
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X <- mu_y + rtensornorm(sample.size, 0, Deltas, sample.axis) # response
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list(X = X, F = F, y = y, sample.axis = sample.axis)
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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", "dist.projection"), # measures
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c("gmlm", "pca", "hopca", "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, eta1, 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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tryCatch({
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time.gmlm <- system.time(
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fit.gmlm <- gmlm_tensor_normal(X, F, sample.axis = sample.axis)
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)["user.self"]
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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.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 <- aperm(F, 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, 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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)["user.self"]
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}, error = function(ex) {
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print(ex)
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})
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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.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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# 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.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.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.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.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\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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