A Path Algorithm for the Fused Lasso Signal Approximator

Abstract

The Lasso is a very well-known penalized regression model, which adds an L1 penalty with parameter λ1 on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L1 penalty with parameter λ2 on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ1 and λ2. We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article.