Adaptive First-Order Methods for General Sparse Inverse Covariance Selection

TL;DR

This paper introduces two adaptive first-order algorithms, ASPG and ANS, for estimating sparse inverse covariance matrices in Gaussian graphical models, demonstrating their efficiency on large-scale problems.

Contribution

The paper develops and compares two novel adaptive first-order methods for sparse inverse covariance estimation, improving scalability and performance over existing approaches.

Findings

Both methods solve large problems with over a thousand variables efficiently.

ASPG generally outperforms ANS in computational experiments.

Methods handle problems with nearly half a million constraints within reasonable time.

Abstract

In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum likelihood estimation problem. Further, we propose an algorithm framework, and develop two first-order methods, that is, the adaptive spectral projected gradient (ASPG) method and the adaptive Nesterov's smooth (ANS) method, for solving this estimation problem. Finally, we compare the performance of these two methods on a set of randomly generated instances. Our computational results demonstrate that both methods are able to solve problems of size at least a thousand and number of constraints of nearly a half million within a reasonable amount of time, and the ASPG method generally outperforms the ANS method.