Efficient proximal gradient algorithms for joint graphical lasso

TL;DR

This paper introduces efficient proximal gradient algorithms for joint graphical lasso, providing a simple, fast, and accurate method for learning multiple graphical models from sparse data.

Contribution

Proposes novel proximal gradient algorithms with closed-form solutions for joint graphical lasso, improving efficiency and accuracy over existing methods.

Findings

Algorithms achieve high accuracy and precision.

Efficiency is competitive with state-of-the-art methods.

Boundedness of solutions and iterations is established.

Abstract

We consider learning an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning for joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterations in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.