# Complex-valued Lasso and graphical Lasso paths This package fits complex-valued Lasso for regression using coordinate descent. The algorithm is extremely fast, and exploits sparsity in the input x matrix where it exists. A variety of predictions can be made from the fitted models. ## Details This package also provides fitting for complex-valued graphical Lasso using coordinate descent. The function is built upon classo with covariate updates, just as the regular real-valued coordinate descent algorithm for graphical Lasso. ||| |:--|:--| |Package:|cxreg| |Type:|Package| |Version:|1.0.0| |Date:|2025-07-01| |License:|MIT + file LICENSE| Very simple to use. Accepts `x,y` data for penalized regression models, and produces the regularization paths over a grid of values for the tuning parameters `lambda`. Similarly, accepts `S,n` data for penalized Gaussian likelihood, and produce the regularization paths over a grid of values for the tuning parameter `lambda`. ## Examples ```r set.seed(1234) x <- array(rnorm(100*20), c(100,20)) + (1+1i) * array(rnorm(100*20), c(100,20)) for (j in 1:20) x[,j] <- x[,j] / sqrt(mean(Mod(x[,j])^2)) e <- rnorm(100) + (1+1i) * rnorm(100) b <- c(1, -1, rep(0, 18)) + (1+1i) * c(-0.5, 2, rep(0, 18)) y <- x %*% b + e fit <- classo(x, y) predict(fit, newx = x[1:5, ], s = c(0.01, 0.005)) predict(fit, type = "coef") plot(fit, xvar = "lambda") p <- 30 n <- 500 C <- diag(0.7, p) C[row(C) == col(C) + 1] <- 0.3 C[row(C) == col(C) - 1] <- 0.3 Sigma <- solve(C) set.seed(1010) m <- floor(sqrt(n)); j <- 1 X_t <- mvtnorm::rmvnorm(n = n, mean = rep(0, p), sigma = Sigma) d_j <- dft.X(X_t,j,m) f_j_hat <- t(d_j) %*% Conj(d_j) / (2*m+1) fit <- cglasso(S=f_j_hat, nobs=n,type="I") plot(fit$Theta_list,index=fit$min_index,type="mod",label=FALSE) ``` ## References Deb, N., Kuceyeski, A., Basu, S. (2024) **Regularized Estimation of Sparse Spectral Precision Matrices**, [https://arxiv.org/abs/2401.11128](https://arxiv.org/abs/2401.11128). ## Author(s) Younghoon Kim, Navonil Deb, Sumanta Basu Maintainer: Younghoon Kim [yk748@cornell.edu](mailto:yk748@cornell.edu)

cxreg-package