A Fast and Flexible Algorithm for the Graph-Fused Lasso

TL;DR

This paper introduces a novel, efficient algorithm for the graph-fused lasso that decomposes graphs into trails, enabling faster computation and greater flexibility in modeling signals over graph structures.

Contribution

The paper presents a trail-based decomposition method for the graph-fused lasso, improving speed and flexibility over existing algorithms.

Findings

Faster convergence compared to previous GFL methods

Flexible in loss function and graph structure choices

Tradeoff between preprocessing time and convergence rate

Abstract

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficiently using techniques for the ordinary (1D) fused lasso. We leverage these trails in a proximal algorithm that alternates between closed form primal updates and fast dual trail updates. The resulting techinque is both faster than previous GFL methods and more flexible in the choice of loss function and graph structure. Furthermore, we present two algorithms for constructing trail sets and show empirically that they offer a tradeoff between preprocessing time and convergence rate.