Complex-Valued Lasso and Complex-Valued Graphical Lasso

Implements 'glmnet'-style complex-valued lasso (CLASSO) and complex-valued graphical lasso (CGLASSO) via a pathwise coordinate descent algorithm for complex-valued parameters, using an isomorphism between complex numbers and 2x2 orthogonal matrices. Also provides a full inference pipeline for high-dimensional sparse spectral precision matrices, including data-driven bandwidth selection, one-step debiasing, asymptotic variance estimation, entry-wise confidence regions, and FDR-controlled hypothesis testing. Supporting tools for cross-validation, simulation, coefficient extraction, and plotting are included. See Deb, Kuceyeski, and Basu (2024) and Deb, Kim, and Basu (2026) .

cxreg: Complex-valued Lasso and Spectral Inference

cxreg provides efficient estimation and inference procedures for complex-valued regression and spectral precision matrix problems.

• CLASSO: complex-valued lasso for penalised regression via pathwise coordinate descent.
• CGLASSO: complex-valued graphical lasso for estimating sparse spectral precision matrices (inverse spectral density matrices).
• Spectral inference pipeline: bandwidth selection, one-step debiasing, asymptotic variance estimation, entry-wise confidence regions, and FDR-controlled hypothesis testing for high-dimensional spectral precision matrices.

Details can be found in Deb, Kuceyeski, and Basu (2024) and 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.

• Download Rtools from: https://cran.r-project.org/bin/windows/Rtools/
• Match the Rtools version to your R version (e.g. Rtools44 for R 4.4.x)

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")

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

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

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:

• A minimal reproducible example
• Session info (sessionInfo())
• R version and OS

References

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