The picasso Package for Nonconvex Regularized M-estimation in High Dimensions in R

We describe an R package named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (Sparse Linear Regression, Sparse Logistic Regression and Sparse Column Inverse Operator), combined with distinct active set identification schemes (truncated cyclic, greedy, randomized and proximal gradient selection). Besides, the package provides the choices between convex (`1 norm) and nonvoncex (MCP and SCAD) regularizations. These methods provide a broad range of options of different sparsity inducing regularizations for most commonly used regression approaches, and various schemes of active set identification allow for the trade-off between statistical consistency and computational efficiency. Moreover, picasso has a provable linear convergence to a unique sparse local optimum with optimal statistical properties, which the competing packages (e.g., ncvreg) do not have. The package is coded in C and can scale up to large problems efficiently with the memory optimized via the sparse matrix output.