cxreg: Complex-valued Lasso and Spectral Inference

cxreg is an R package, available on CRAN, that provides efficient estimation and inference procedures for complex-valued regression and spectral precision matrix problems.

The estimation algorithms and their implementation in cxreg are described in Kim, Deb, and Basu (2026), with the underlying methodology developed in Deb, Kuceyeski, and Basu (2024). The spectral inference procedures are developed in Deb, Kim, and Basu (2026).

Installation

Windows

Before installing via devtools, ensure you have the correct version of Rtools installed. Rtools is required to compile C/C++/Fortran code in R packages on Windows.

macOS

Install GCC (which includes gfortran) via Homebrew:

brew install gcc

Check whether ~/.R exists:

ls -ld ~/.R

If not, create it and open ~/.R/Makevars:

mkdir ~/.R
vim ~/.R/Makevars

Add the following lines, replacing 15.0.1 with the version returned by gfortran --version:

FC    = /opt/homebrew/Cellar/gcc/15.0.1/bin/gfortran
F77   = /opt/homebrew/Cellar/gcc/15.0.1/bin/gfortran
FLIBS = -L/opt/homebrew/Cellar/gcc/15.0.1/lib/gcc/15

Install from GitHub

# install.packages("devtools")
# devtools::install_github("yk748/cxreg")
install.packages("cxreg", repos = c('https://yk748.r-universe.dev', 'https://cloud.r-project.org'))

Quick start

CLASSO: complex-valued lasso regression

library(cxreg)

data(classo_example)
x <- classo_example$x   # complex matrix, 1000 x 200
y <- classo_example$y   # complex vector, length 1000

# Fit lasso path
fit <- classo(x, y)
print(fit)
plot(fit, xvar = "lambda")

# Cross-validation
cvfit <- cv.classo(x, y, trace.it = 1)
print(cvfit)
plot(cvfit)

# Coefficients and predictions at optimal lambda
coef(cvfit, s = "lambda.min")
predict(cvfit, newx = x[1:5, ], s = "lambda.min")

CGLASSO: complex-valued graphical lasso

data(cglasso_example)
f_hat <- cglasso_example$f_hat   # p x p complex spectral density matrix
m     <- cglasso_example$m       # half-bandwidth

fit <- cglasso(S = f_hat, m = m, type = "I")
print(fit)
plot(fit, index = fit$min_index, type = "mod")

Spectral inference pipeline

library(mvtnorm)
set.seed(42)
p <- 10; n <- 200
X <- rmvnorm(n, mean = rep(0, p), sigma = diag(p))

# 1. Data-driven bandwidth selection
bw_sel <- select_m(X)
m <- bw_sel$m_opt

# 2. Smoothed periodogram and cglasso fit
j    <- floor(n / 4)
dft  <- dft.all(X)
fhat <- fhat_at(dft, j, m)
fit  <- cglasso(S = fhat, m = m)

# 3. One-step debiasing
res  <- decglasso(object = fit, fhat = fhat)

# 4. Asymptotic variance estimation
vc   <- var.cov(Theta = res$Theta_tilde, X = X, j = j, m = m,
                type = "plug-in")

# 5. Entry-wise test statistics and confidence regions (H0: Theta = 0)
st   <- spec.test(Est = res$Theta_tilde, varcov = vc, m = m, alpha = 0.05)

# 6. FDR-controlled support recovery
fdr  <- spec.fdr(Chi_sq = st$Chi_sq, alpha = 0.05, diag = FALSE)
fdr$tau
fdr$Decision

Function reference

Category Function Description
Regression classo() Fit complex lasso path
Regression cv.classo() k-fold cross-validation for classo
Regression coef.classo() Extract coefficients
Regression predict.classo() Predict fitted values or coefficients
Regression print.classo() Print coefficient path summary
Regression plot.classo() Plot coefficient paths (Re and Im panels)
Graphical lasso cglasso() Fit complex graphical lasso path
Graphical lasso plot.cglasso() Heatmap of estimated precision matrix
Spectral utilities dft.all() Full normalised DFT of a time series matrix
Spectral utilities dft.j() DFT windowed around a single frequency
Spectral utilities fhat_at() Smoothed periodogram at a frequency index
Bandwidth selection select_m() GCV-based half-bandwidth selection
Inference decglasso() One-step debiased spectral precision estimator
Inference var.cov() Plug-in or HAC variance/pseudovariance estimation
Inference spec.test() Z-statistics, chi-squared statistics, CI half-widths
Inference spec.fdr() FDR-controlled multiple testing

Parallel cross-validation

cv.classo() supports parallel fold fitting via the parallel = TRUE argument. Register a backend before calling:

library(doParallel)
registerDoParallel(cores = 4)
cvfit <- cv.classo(x, y, parallel = TRUE)

Any foreach-compatible backend (doMC, doFuture, etc.) is supported.

Version history

Version Date Notes
1.1.4 2026-07-09 Added the inference vignette covering the full spectral inference pipeline
1.1.2 2026-06-27 Fixed vignette API calls and compilation issues
1.1.1 2026-06-26 Reduced vignette PDF size for CRAN compatibility
1.1.0 2026-06-01 Added spectral inference pipeline: select_m, decglasso, var.cov, spec.test, spec.fdr
1.0.0 2025-07-01 Initial release: CLASSO, CGLASSO, cross-validation, plotting

Reporting issues

If you encounter a bug or have a feature request, please open an issue at https://github.com/yk748/cxreg/issues or email Younghoon Kim at ykim124@ua.edu.

Please include:

References

Younghoon Kim, Navonil Deb, and Sumanta Basu. 2026. "cxreg: An R Package for Complex-Valued Lasso and Graphical Lasso." Journal of Open Source Software 11(124): 9698. https://doi.org/10.21105/joss.09698.

Navonil Deb, Amy Kuceyeski, and Sumanta Basu. 2024. "Regularized Estimation of Sparse Spectral Precision Matrices." arXiv preprint arXiv:2401.11128. https://arxiv.org/abs/2401.11128.

Navonil Deb, Younghoon Kim, and Sumanta Basu. 2026. "Inference for High-Dimensional Sparse Spectral Precision Matrices." arXiv preprint arXiv:2606.07986. https://arxiv.org/abs/2606.07986.

Jerome Friedman, Trevor Hastie, Holger Hofling, and Robert Tibshirani. 2007. "Pathwise Coordinate Optimization." The Annals of Applied Statistics 1(2): 302–332. https://doi.org/10.1214/07-AOAS131

Jerome Friedman, Trevor Hastie, and Robert Tibshirani. 2008. "Sparse Inverse Covariance Estimation with the Graphical Lasso." Biostatistics 9(3): 432–441. https://doi.org/10.1093/biostatistics/kxm045

Jerome Friedman, Trevor Hastie, and Robert Tibshirani. 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent." Journal of Statistical Software 33(1): 1–22. https://doi.org/10.18637/jss.v033.i01