# Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics

arXiv: https://arxiv.org/abs/2607.18559 · HTML: https://mlsanity.com/paper/2607.18559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 52 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [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)
- [Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics](https://mlsanity.com/paper/2104.00995/) (2021)
- [Better Models and Algorithms for Learning Ising Models from Dynamics](https://mlsanity.com/paper/2507.15173/) (2025)
- [A mixing time bound for Gibbs sampling from log-smooth log-concave distributions](https://mlsanity.com/paper/2412.17899/) (2024)
- [Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics](https://mlsanity.com/paper/2412.18594/) (2024)
- [Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing](https://mlsanity.com/paper/2606.31230/) (2026)

## Abstract (arXiv)

Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the mixing time of the chain, which can be super-polynomial in the dimension p without strong assumptions, or are suboptimal in the minimum normalized edge strength kappa. We propose two algorithms that are mixing-free and attain the kappa-2 dependence of the information-theoretic lower bounds. Both instantiate a shared dueling-neighborhood search meta-algorithm with a local statistic built directly from the update sequence. For every fixed precision matrix and deterministic initialization, the first algorithm fits a least-squares regression at the updates of each node and has pointwise recovery horizon widetilde O(pd2/kappa2), where d is the maximum degree. Its horizon depends logarithmically on a local conditioning quantity and on the initialization potential. The second algorithm is based on counting occurences of a specific update pattern and requires widetilde O(pd4/kappa2) updates, with no dependence on any condition number. The central technical challenge is that both statistics are built from dependent, non-stationary observations. Our analysis tackles this by demonstrating how to extract fresh Gaussian innovations from the update sequence, which yields mixing-free control of appropriate quantities. Neither the algorithms nor their analyses invoke stationarity, a spectral gap, or mixing conditions.