Learning conditional independence structure for high-dimensional uncorrelated vector processes

TL;DR

This paper introduces a method for inferring the conditional independence graph of high-dimensional, nonstationary Gaussian time series using conditional variance testing, effective even with limited samples.

Contribution

It proposes a novel graphical model selection technique tailored for high-dimensional, nonstationary Gaussian processes with finite samples, and provides theoretical guarantees for its success.

Findings

Method successfully infers conditional independence graphs in high-dimensional settings.

Sample size requirements are characterized for high-probability success.

Approach handles nonstationary processes with time-varying distributions.

Abstract

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal distribution. The selection method is based on testing conditional variances obtained for small subsets of process components. This allows to cope with the high-dimensional regime, where the sample size can be (drastically) smaller than the process dimension. We characterize the required sample size such that the proposed selection method is successful with high probability.