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

arXiv: https://arxiv.org/abs/2412.18594 · HTML: https://mlsanity.com/paper/2412.18594/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 10 of 10)

- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Learning graphical models from the Glauber dynamics](https://mlsanity.com/paper/1410.7659/) (2014)
- [A Unified Approach to Learning Ising Models: Beyond Independence and Bounded Width](https://mlsanity.com/paper/2311.09197/) (2023)
- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [Statistically efficient thinning of a Markov chain sampler](https://mlsanity.com/paper/1510.07727/) (2015)
- [MCMC-Based Inference in the Era of Big Data: A Fundamental Analysis of the Convergence Complexity of High-Dimensional Chains](https://mlsanity.com/paper/1508.00947/) (2015)
- [Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics](https://mlsanity.com/paper/2104.00995/) (2021)
- [A mixing time bound for Gibbs sampling from log-smooth log-concave distributions](https://mlsanity.com/paper/2412.17899/) (2024)
- [Graphical Models for Financial Time Series and Portfolio Selection](https://mlsanity.com/paper/2101.09214/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing](https://mlsanity.com/paper/2606.31230/) (2026)
- [Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics](https://mlsanity.com/paper/2607.18559/) (2026)

## Abstract (arXiv)

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.