tensor_predictors/sim/sim_1b_normal_2.R

library(tensorPredictors)
# library(RGCCA)
### Load modified version which _does not_ create a clusster in case of
### `n_cores == 1` allowing huge speed improvements! (at least on Ubuntu 22.04 LTS)
### Moreover, it is compatible with `Rscript`
### Also added `Encoding: UTF-8` in `DESCRIPTION`
devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)


setwd("~/Work/tensorPredictors/sim/")
base.name <- format(Sys.time(), "sim_1b_normal-%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(0x1bL, "Mersenne-Twister", "Inversion", "Rejection")

### Simulation configuration
reps <- 100                     # number of simulation replications
sample.sizes <- c(100, 200, 300, 500, 750)  # sample sizes `n`
validation.sizes <- 10000
dimX <- c(2, 3, 5)              # predictor `X` dimension
dimF <- rep(2, length(dimX))    # "function" `F(y)` of responce `y` dimension

# setup true model parameters
betas <- Map(diag, 1, dimX, dimF)
Omegas <- Map(function(pj) 0.5^abs(outer(1:pj, 1:pj, `-`)), dimX)   # AR(0.5)
eta1 <- 0

# data sampling routine
sample.data <- function(sample.size, eta1, betas, Omegas) {
    # responce is a standard normal variable
    y <- rnorm(sample.size)
    # F(y) is a tensor of monomials
    F <- sapply(y, function(yi) Reduce(outer, Map(`^`, yi, Map(seq, 0, len = dimF))))
    dim(F) <- c(dimF, sample.size)

    # sample predictors from tensor normal X | Y = y (last axis is sample axis)
    sample.axis <- length(betas) + 1L
    Deltas <- Map(solve, Omegas)                            # normal covariances
    mu_y <- mlm(mlm(F, betas) + as.vector(eta1), Deltas)    # conditional mean
    X <- mu_y + rtensornorm(sample.size, 0, Deltas, sample.axis)    # response

    list(X = X, F = F, y = y, sample.axis = sample.axis)
}

# 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("dist.subspace", "dist.projection"),                  # measures
            c("gmlm", "tsir", "hopca"),                             # methods
            paste, sep = "."
        ), outer(
            c("time", "dist.min.subspace", "dist.min.projection", "reconst.error"),  # measures
            c("gmlm", "pca", "hopca", "tsir", "mgcca"),             # methods
            paste, sep = "."
    ))
)

# compute true (full) model parameters to compair estimates against
B.true <- Reduce(`%x%`, rev(betas))
minimal <- function(B) { cbind(
    "1"   = B[, 1],
    "y"   = rowSums(B[, c(2, 3, 5)]),
    "y^2" = rowSums(B[, c(4, 6, 7)]),
    "y^3" = B[, 8]
) }
B.min.true <- minimal(B.true)

### 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, eta1, betas, Omegas)

        # 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
        tryCatch({
            time.gmlm <- system.time(
                fit.gmlm <- gmlm_tensor_normal(X, F, sample.axis = sample.axis)
            )["user.self"]
            time.pca <- system.time(
                fit.pca <- prcomp(mat(X, sample.axis), rank. = 4)
            )["user.self"]
            time.hopca <- system.time(
                fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
            )["user.self"]
            time.tsir <- system.time(
                fit.tsir <- TSIR(X, y, dimF, sample.axis = sample.axis)
            )["user.self"]
            # `mgcca` expects the first axis to be the sample axis
            X.perm <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
            F.min <- mat(F, sample.axis)[, c(2, 4, 8)]
            time.mgcca <- system.time(
                fit.mgcca <- mgcca(
                    list(X.perm, F.min), # `drop` removes 1D axis
                    quiet = TRUE,
                    scheme = "factorial",
                    ncomp = c(4, 1)
                )
            )["user.self"]
        }, error = function(ex) {
            print(ex)
        })

        # Compute true reduction matrix
        B.gmlm <- with(fit.gmlm, Reduce(`%x%`, rev(betas)))
        B.hopca <- Reduce(`%x%`, rev(fit.hopca))
        B.tsir <- Reduce(`%x%`, rev(fit.tsir))

        # and minimal true reductions if not already minimal
        B.min.gmlm <- minimal(B.gmlm)
        B.min.pca <- fit.pca$rotation
        B.min.hopca <- B.hopca[, 1:4]
        B.min.tsir <- La.svd(B.tsir, 4L, 0L)$u
        B.min.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.hopca <- dist.subspace(B.true, B.hopca, normalize = TRUE)
        dist.subspace.tsir  <- dist.subspace(B.true, B.tsir,  normalize = TRUE)

        dist.min.subspace.gmlm  <- dist.subspace(B.min.true, B.min.gmlm,  normalize = TRUE)
        dist.min.subspace.pca   <- dist.subspace(B.min.true, B.min.pca,   normalize = TRUE)
        dist.min.subspace.hopca <- dist.subspace(B.min.true, B.min.hopca, normalize = TRUE)
        dist.min.subspace.tsir  <- dist.subspace(B.min.true, B.min.tsir,  normalize = TRUE)
        dist.min.subspace.mgcca <- dist.subspace(B.min.true, B.min.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.hopca <- dist.projection(B.true, B.hopca)
        dist.projection.tsir  <- dist.projection(B.true, B.tsir)

        dist.min.projection.gmlm  <- dist.projection(B.min.true, B.min.gmlm)
        dist.min.projection.pca   <- dist.projection(B.min.true, B.min.pca)
        dist.min.projection.hopca <- dist.projection(B.min.true, B.min.hopca)
        dist.min.projection.tsir  <- dist.projection(B.min.true, B.min.tsir)
        dist.min.projection.mgcca <- dist.projection(B.min.true, B.min.mgcca)

        # # Reconstruction error (MSE) of y given X with a new sample
        # c(X, F, y, sample.axis) %<-% sample.data(validation.sizes, eta1, betas, Omegas)
        # y.gmlm <- rowMeans(mat(mlm(X, fit.gmlm$betas), sample.axis)[, c(2, 3, 5)])


        # Call CSV logger writing results to file
        logger()

        # print progress
        cat(sprintf("sample size (%d): %d/%d - rep: %d/%d\n",
            sample.size, which(sample.size == sample.sizes),
            length(sample.sizes), rep, reps))
    }
}


### read simulation results and generate plots
if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }

sim <- read.csv(log.file)

plot.sim(sim, "dist.subspace", main = "Full Subspace Distance",
    xlab = "Sample Size", ylab = "Distance")

plot.sim(sim, "dist.min.subspace", main = "Min Subspace Distance",
    xlab = "Sample Size", ylab = "Distance")

plot.sim(sim, "dist.projection", main = "Full Projection Distance",
    xlab = "Sample Size", ylab = "Distance")

plot.sim(sim, "dist.min.projection", main = "Min Projection Distance",
    xlab = "Sample Size", ylab = "Distance")

plot.sim(sim, "time", main = "Runtime",
    xlab = "Sample Size", ylab = "Time")