# Learning graphical models from the Glauber dynamics

arXiv: https://arxiv.org/abs/1410.7659 · HTML: https://mlsanity.com/paper/1410.7659/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2014.

## Built on by (most cited first, 14 of 14)

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- [The Benefits of Temporal Correlations: SGD Learns k-Juntas from Random Walks Efficiently](https://mlsanity.com/paper/2605.10237/) (2026)
- [Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing](https://mlsanity.com/paper/2606.31230/) (2026)
- [Data-Driven Interaction Analysis of Line Failure Cascading in Power Grid Networks](https://mlsanity.com/paper/2112.01061/) (2021)
- [One-Shot Learning for k-SAT](https://mlsanity.com/paper/2502.07135/) (2025)
- [A packing lemma for VCNk-dimension and learning high-dimensional data](https://mlsanity.com/paper/2505.15688/) (2025)
- [Learning CNF Formulas from Uniform Random Solutions: Near-Tight Sample Complexity for Valiant's Algorithm](https://mlsanity.com/paper/2609.15268/) (2026)

## Abstract (arXiv)

In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a graphical model and it is frequently used to sample from the stationary distribution (to which it converges given sufficient time). Additionally, the Glauber dynamics is a natural dynamical model in a variety of settings. This work deviates from the standard formulation of graphical model learning in the literature, where one assumes access to i.i.d. samples from the distribution. Much of the research on graphical model learning has been directed towards finding algorithms with low computational cost. As the main result of this work, we establish that the problem of reconstructing binary pairwise graphical models is computationally tractable when we observe the Glauber dynamics. Specifically, we show that a binary pairwise graphical model on p nodes with maximum degree d can be learned in time f(d)p2log p, for a function f(d), using nearly the information-theoretic minimum number of samples.