A decomposition method for lasso problems with zero-sum constraint

TL;DR

This paper introduces a new algorithm for solving high-dimensional lasso problems with zero-sum constraints, combining active-set and coordinate descent techniques, with proven convergence and demonstrated effectiveness.

Contribution

A novel algorithm tailored for zero-sum constrained lasso problems that integrates active-set and coordinate descent methods, with theoretical convergence guarantees.

Findings

Proven global convergence of the algorithm.

Effective performance on synthetic and real datasets.

Software implementation is publicly available.

Abstract

In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set technique, to identify the zero variables in the optimal solution, with a 2-coordinate descent scheme. At every iteration, the algorithm chooses between two different strategies: the first one requires to compute the whole gradient of the smooth term of the objective function and is more accurate in the active-set estimate, while the second one only uses partial derivatives and is computationally more efficient. Global convergence to optimal solutions is proved and numerical results are provided on synthetic and real datasets, showing the effectiveness of the proposed method. The software is publicly available.