The PICASSO Package for High Dimensions Nonconvex Sparse Learning in R

• Activity Number: 21
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xingguo Li* and Tuo Zhao and Tong Zhang and Han Liu
• Companies: and The Johns Hopkins University and Rutgers University and Princeton
• Keywords: Pathwise Coordinate Optimization ; Nonconvex Sparse Learning ; Statistical and Computational Trade-off

Abstract

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 (L1 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.