Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series

TL;DR

This paper introduces a non-convex sparse-group log-sum penalty for estimating the inverse power spectral density in high-dimensional Gaussian time series, providing convergence guarantees and demonstrating effectiveness with synthetic and real data.

Contribution

It proposes a novel sparse-group log-sum penalty approach with an ADMM algorithm for better CIG inference in time series, with convergence analysis and empirical validation.

Findings

The method converges locally under certain conditions.

It achieves accurate inverse PSD estimation in experiments.

Demonstrated effectiveness on synthetic and real datasets.

Abstract

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.