Abstract
Local samplers are algorithms that generate random samples based on local queries to high-dimensional distributions, ensuring the samples follow the correct induced distributions while maintaining time complexity that scales locally with the query size. These samplers have broad applications, including deterministic approximate counting [He, Wang, Yin, SODA ‘23; Feng et al., FOCS ‘23], sampling from infinite or high-dimensional Gibbs distributions [Anand, Jerrum, SICOMP ‘22; He, Wang, Yin, FOCS ‘22], and providing local access to large random objects [Biswas, Rubinfeld, Yodpinyanee, ITCS ‘20].
In this work, we present local samplers for Gibbs distributions of spin systems. Specifically, we design linear-time local samplers for:
• spin systems with soft constraints, including the first local sampler for near-critical Ising models;
• truly repulsive spin systems, represented by the first local sampler for uniform proper $q$-colorings, with $q=O(\Delta)$ colors on graphs with maximum degree $\Delta$.
These local samplers are efficient beyond the “local uniformity” threshold, which imposes unconditional marginal lower bounds—a key assumption required by all prior local samplers. Our results show that, in general, local sampling is not significantly harder than global sampling for spin systems. As an application, our results also imply local algorithms for probabilistic inference in the same near-critical regimes.
Hongyang Liu
Ph.D. Student
I am a Ph.D. student in the Theory Group at the School of Computer Science, Nanjing University.
Chunyang Wang
Postdoc
I am Chunyang Wang (王淳扬), currently a project researcher (postdoc) at the National Institute of Informatics (NII), hosted by Prof. Yuichi Yoshida. My research interests broadly lie in theoretical computer science, especially algorithms for counting and sampling and algorithmic stability.
Yitong Yin
Professor
I am a professor in the Theory Group at the School of Computer Science, Nanjing University. My research interests include randomized algorithms and computational sampling and counting, data structures and lower bounds, and parallel and distributed computing.