T-Rex Selector: High-Dimensional Variable Selection & FDR Control

Variable selection for regression and classification in high-dimensional settings with control of the false discovery rate (FDR) at a user-specified target level. The implementations are primarily based on the T-Rex selector of Machkour, Muma and Palomar (2025) and its dependency-aware extension for correlated variables by Machkour, Muma and Palomar (2025) . Since version 2.0.0 the package comes as R bindings to the 'TRexSelector' C++ library, which replaces the pure-R implementation of the 1.x releases.

TRexSelector

Title: The T-Rex selector for fast high-dimensional variable selection with FDR control

Description: It performs fast variable selection in large-scale high-dimensional settings while controlling the false discovery rate (FDR) at a user-defined target level. Since version 2.0.0 the R package provides bindings to the TRexSelector C++ library, which replaces the pure-R implementation of the 1.x releases under the same package name.

Papers: The package is based on the papers

J. Machkour, M. Muma, and D. P. Palomar, “The terminating-random experiments selector: Fast high-dimensional variable selection with false discovery rate control,” Signal Processing, vol. 231, article 109894, 2025. (https://doi.org/10.1016/j.sigpro.2025.109894)

J. Machkour, M. Muma, and D. P. Palomar, “High-dimensional false discovery rate control for dependent variables,” Signal Processing, vol. 234, article 109990, 2025. (https://doi.org/10.1016/j.sigpro.2025.109990)

Note: The T-Rex selector performs terminated-random experiments (T-Rex) using the T-LARS algorithm and fuses the selected active sets of all random experiments to obtain a final set of selected variables. The T-Rex selector provably controls the false discovery rate (FDR), i.e., the expected fraction of selected false positives among all selected variables, at the user-defined target level while maximizing the number of selected variables and, thereby, achieving a high true positive rate (TPR) (i.e., power). The T-Rex selector can be applied in various fields, such as genomics, financial engineering, or any other field that requires a fast and FDR-controlling variable/feature selection method for large-scale high-dimensional settings.

In the following sections, we show you how to install and use the package.

Installation

The package compiles its C++ backend on installation, so a C++20-capable compiler is required (GCC ≥ 10, Clang ≥ 12, Apple Clang ≥ 14, or Rtools on Windows), together with R ≥ 4.3.

OpenMP is optional. Without it the package compiles single-threaded and trex_get_max_threads() returns 1. On Linux and Windows, R supplies the OpenMP flags. CRAN’s R for macOS has none, so configure compiles with the omp.h of Homebrew’s libomp (brew install libomp) and links R’s own OpenMP runtime (lib/libomp.dylib of the R installation, the one other packages load), or Homebrew’s runtime when R ships none. Setting TREX_OPENMP=no forces the single-threaded build, for example TREX_OPENMP=no R CMD INSTALL R/TRexSelector.

First install the R-side prerequisites (once, from an R session):

install.packages(c("Rcpp", "RcppEigen", "BH", "Rcereal", "R6"))

Then install ‘TRexSelector’ from GitHub — the package lives in the R/TRexSelector/ subdirectory of the repository:

# Option 1: Install directly from GitHub
install.packages("remotes")
remotes::install_github("trexselector/TRexSelector", subdir = "R/TRexSelector")

# Option 2: Install from a local clone of the repository
# (from the shell, at the repository root)
# R CMD INSTALL R/TRexSelector

(CRAN still carries the pure-R 1.x release. The submission of version 2.0.0 is in progress, and once it is accepted, install.packages("TRexSelector") provides the C++-backed package.)

You can open the help pages with:

library(TRexSelector)
help(package = "TRexSelector")
?TRexSelector
?trex_control
?trex_fdp
?trex_tpp
# etc.

To cite the package ‘TRexSelector’ in publications use:

citation("TRexSelector")

Quick Start

This section illustrates the basic usage of the ‘TRexSelector’ package to perform FDR-controlled variable selection in large-scale high-dimensional settings based on the T-Rex selector.

1. First, we generate a high-dimensional Gaussian data set with sparse support:

library(TRexSelector)

# Setup
n <- 75 # number of observations
p <- 150 # number of variables
num_act <- 3 # number of true active variables
beta <- c(rep(1, times = num_act), rep(0, times = p - num_act)) # coefficient vector
true_actives <- which(beta > 0) # indices of true active variables

# Generate Gaussian data
set.seed(123)
X <- matrix(stats::rnorm(n * p), nrow = n, ncol = p)
y <- X %*% beta + stats::rnorm(n)

1. Second, we perform FDR-controlled variable selection using the T-Rex selector for a target FDR of 5%. The selectors are R6 classes: construct with $new(...), run with $select(), and read the results from active fields such as $selected_indices (1-based indices):

# Seed
set.seed(1234)

# Variable selection via T-Rex
sel <- TRexSelector$new(X, y, tFDR = 0.05, verbose = FALSE)
sel$select()

paste0("True active variables: ", paste(as.character(true_actives), collapse = ", "))
#> [1] "True active variables: 1, 2, 3"
paste0("Selected variables:    ", paste(as.character(sel$selected_indices), collapse = ", "))
#> [1] "Selected variables:    1, 2, 3"

So, for a preset target FDR of 5%, the T-Rex selector has selected all true active variables and there are no false positives in this example.

Note that users have to choose the target FDR according to the requirements of their specific applications.

All selector variants (TRexSelector, TRexDASelector, TRexGVSSelector, TRexScreeningSelector, TRexBiobankScreeningSelector, TRexSPCASelector) follow the same construct → $select() → inspect pattern.

Dummy Strategies

The T-Rex selector calibrates the number of dummies in its L-loop. trex_control(lloop_strategy = ) says how the dummies of that loop are produced, in every selector that takes the control.

"STANDARD" draws fresh dummies at every step, the law of the T-Rex paper and the default on every surface. The seeded strategies store nothing and suit designs where K times L times p columns do not fit in memory. "SEEDED" selects exactly as "STANDARD" for the same seed, and "PERMUTATION_SEEDED" exactly as "PERMUTATION". "HCONCAT" keeps the grown law, which calibrates a larger L and gains 0.6 percentage points of true positive rate (TPR) on average in a paired study of 500 trials, at the same false discovery rate (FDR). "SKIPL" fixes L at the cap and skips the calibration, and under a large fixed L without the stagnation stop its FDP estimate is anti-conservative (the selector warns from max_dummy_multiplier = 10 on), so the calibrated strategies are the safe choice. The dummies are standard Normal by default, and trex_dummy_distribution() offers the other laws. Vignette page 2, vignette("v02-trex-selector"), carries the study and the seeds section.

Threads

The package runs serially by default: trex_control() has parallel_rnd_experiments = FALSE, max_outer_threads = 1 and max_inner_threads = 1, and tsolver_options() has n_threads = 1. The random experiments of a selector run one after the other, every T-solver on one thread. Parallel work is opt-in, and one layer owns the cores at a time.

• trex_control(parallel_rnd_experiments = TRUE, max_outer_threads = m) runs the K random experiments on m threads, at most K. Inside the parallel experiments every solver runs serially.
• trex_control(max_inner_threads = m) gives the solvers inside the experiments a budget of m threads for their passes over the design. The budget is live when the experiments run in sequence, which the lean L-loop strategies ("SEEDED", "PERMUTATION", "PERMUTATION_SEEDED") always do. A pass is split only when it touches at least a million entries of the design, because the cost of forming a team of threads exceeds the gain below that. Two to four threads carry the gain, since the passes are memory-bandwidth bound. The seeded generators (the dummies, the synthetic designs) count their work in the same unit with the measured cost of a random draw (about 80 entries) and of seeding an engine (up to 32,000), so they split from a few thousand entries.
• tsolver_options(n_threads = m) is the same budget for a T-solver used on its own, and $set_num_threads() changes it on a live solver.
• Every other kernel (the scalers, the clustering, the ML regressions, trex_normalize_design(), the dummy and data generators) runs on the library’s default budget, which starts at 1, so the package is single-threaded by default on every machine. trex_set_num_threads(m) sets that default for the session and returns the previous value, trex_get_num_threads() reads it, and the n_threads argument of the scalers, the clustering and the ML classes overrides it per object. Inside a selector these kernels take max_inner_threads. trex_get_max_threads() reports the threads OpenMP can run on the machine, an upper bound for a budget.

Every thread option is a whole number of at least 1; other values are errors. A seeded run selects the same variables whatever the thread settings. Without OpenMP every setting is a no-op and trex_get_max_threads() returns 1 (see Installation). The parallelism vignette has the details.

Documentation

The package has twelve vignettes in vignettes/ (built on installation with build_vignettes = TRUE, listed by browseVignettes("TRexSelector")): getting started, the T-Rex selector, T-Rex+DA, T-Rex GVS, screening, T-Rex SPCA, T-Rex Tikhonov, the T-solvers, the ML methods, memory mapping, working without data copies, and parallelism. The help page of every selector, T-solver and machine learning class ends with the papers it builds on, and citation("TRexSelector") lists the package entry and the T-Rex method papers.

Links

T-Rex paper: https://doi.org/10.48550/arXiv.2110.06048

TRexSelector repository (C++ core, Python, and R packages): GitHub-TRexSelector

Bug reports: GitHub Issues

Acknowledgements

The package builds on the Eigen linear algebra library: G. Guennebaud, B. Jacob et al., Eigen v3, https://libeigen.gitlab.io/, 2010. It binds the C++ core through Rcpp and RcppEigen and relies on cereal (Rcereal) for serialization and on Boost.Interprocess (BH) for memory mapping, with OpenMP for the threads where the toolchain provides it.

License

GPL ≥ 3 — see the GNU General Public License v3.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. It is distributed WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.