An Alternating Direction Method of Multipliers Algorithm for the Weighted Fused LASSO Signal Approximator

TL;DR

This paper introduces an efficient ADMM algorithm for the Weighted Fused LASSO Signal Approximator, reducing computational complexity from $O(p^4)$ to $O(p^2)$ and providing an accessible R package.

Contribution

The paper develops a specialized ADMM algorithm for wFLSA that significantly improves computational efficiency over existing methods.

Findings

Reduces algorithm complexity from $O(p^4)$ to $O(p^2)$

Provides an open-source R package for implementation

Reformulates wFLSA as a Generalized LASSO problem

Abstract

We present an Alternating Direction Method of Multipliers (ADMM) algorithm designed to solve the Weighted Generalized Fused LASSO Signal Approximator (wFLSA). First, we show that wFLSAs can always be reformulated as a Generalized LASSO problem. With the availability of algorithms tailored to the Generalized LASSO, the issue appears to be, in principle, resolved. However, the computational complexity of these algorithms is high, with a time complexity of $O(p^4)$ for a single iteration, where $p$ represents the number of coefficients. To overcome this limitation, we propose an ADMM algorithm specifically tailored for wFLSA-equivalent problems, significantly reducing the complexity to $O(p^2)$. Our algorithm is publicly accessible through the R package wflsa.