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

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
1.1.0	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:

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