Learning to Sample from Censored Markov Random Fields

TL;DR

This paper introduces an algorithm for learning censored Markov Random Fields without assumptions on graph structure, achieving near-optimal accuracy in high-temperature regimes and providing computational lower bounds.

Contribution

The paper presents a novel algorithm for learning high-temperature CMRFs that does not require prior structural assumptions, with strong theoretical guarantees.

Findings

Algorithm achieves o(n) transportation distance

No assumptions on graph structure or observed node locations

Lower bounds show limits of possible improvements

Abstract

We study learning Censor Markov Random Fields (abbreviated CMRFs). These are Markov Random Fields where some of the nodes are censored (not observed). We present an algorithm for learning high-temperature CMRFs within o(n) transportation distance. Crucially our algorithm makes no assumption about the structure of the graph or the number or location of the observed nodes. We obtain stronger results for high girth high-temperature CMRFs as well as computational lower bounds indicating that our results can not be qualitatively improved.