Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics

TL;DR

This paper introduces two methods for Gaussian graphical model selection from dependent Glauber dynamics data, including a local correlation test and a subsampling approach, with theoretical guarantees and empirical comparisons.

Contribution

It develops novel algorithms for structure learning from dependent samples, including a parallelizable edge test and a subsampling reduction under contraction conditions.

Findings

The local estimator does not require mixing time and is parallelizable.

The subsampling approach allows standard i.i.d. learners to be applied to dependent data.

Finite-sample guarantees and lower bounds on observation time are established.

Abstract

Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian Glauber dynamics. We develop two complementary approaches. The first is a local edge-testing estimator based on an appropriately designed correlation test that reveals edges. This estimator does not require waiting for the chain to mix and admits an embarrassingly parallel edgewise implementation. The second is a burn-in/thinning reduction: under a Dobrushin contraction condition, we prove that a suitably subsampled Gaussian Gibbs trajectory is close in total variation to an i.i.d. product sample, allowing standard i.i.d. Gaussian graphical model learners to be used as black boxes. The key technical ingredient, which may be of independent interest, is a high-dimensional total-variation bound for random-scan Gaussian Gibbs samplers, obtained by combining Wasserstein contraction with an approximate Lipschitz smoothing argument. We prove finite-sample recovery guarantees for both approaches, establish information-theoretic lower bounds on the observation time, and empirically compare the resulting sample-computation tradeoffs.