Efficient Implementations of the Generalized Lasso Dual Path Algorithm

TL;DR

This paper presents optimized algorithms for the generalized lasso dual path, improving efficiency and stability, with implementations available in the genlasso R package for various problem types.

Contribution

It introduces fast, specialized implementations for trend filtering, fused lasso, and sparse fused lasso problems, enhancing computational performance.

Findings

Significant speed improvements over generic methods

Enhanced numerical stability in specialized algorithms

Available in the genlasso R package for practical use

Abstract

We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filtering problems, fused lasso problems, and sparse fused lasso problems, both with X=I and a general matrix X. These specialized implementations offer a considerable improvement over the generic implementation, both in terms of numerical stability and efficiency of the solution path computation. These algorithms are all available for use in the genlasso R package, which can be found in the CRAN repository.