Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation

TL;DR

This paper introduces a novel multi-attribute graph estimation method for high-dimensional multivariate Gaussian time series, leveraging ADMM to improve the detection of conditional independence graphs over existing frequency-domain techniques.

Contribution

It formulates the problem as multi-attribute graph estimation with a sparse-group lasso approach and provides an ADMM-based solution with theoretical analysis.

Findings

Outperforms existing frequency-domain methods in edge detection accuracy.

Provides a theoretical analysis of the proposed estimation approach.

Numerical results validate the effectiveness of the method.

Abstract

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.