A Path Algorithm for the Fused Lasso Signal Approximator

The Lasso is a very well-known penalized regression model, which adds an L-1 penalty with parameter lambda(1) on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L-1 penalty with parameter lambda(2) 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 lambda(1) and lambda(2). 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.