The solution path of the generalized lasso

TL;DR

This paper introduces a path algorithm for the generalized lasso problem, enabling efficient computation of solutions for various applications by solving its dual and estimating degrees of freedom.

Contribution

It develops a dual-based path algorithm for the generalized lasso and provides an unbiased degrees of freedom estimate, extending existing methods like LARS.

Findings

The algorithm efficiently computes the entire solution path.

Connection established between the generalized lasso and LARS for D=I.

Provides an intuitive degrees of freedom estimate for various D.

Abstract

We present a path algorithm for the generalized lasso problem. This problem penalizes the $\ell_1$ norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which greatly facilitates computation of the path. For $D=I$ (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.