GiSS: Combining Gibbs sampling and SampleSearch for inference in mixed probabilistic and deterministic graphical models

Abstract

Mixed probabilistic and deterministic graphical models are ubiquitous in real-world applications. Unfortunately, Gibbs sampling, a popular MCMC technique, does not converge to the correct answers in presence of determinism and the refore cannot be used for inference in such models. In this paper, we propose to remedy this problem by combining Gibbs sampling with Sample Search, an advanced importance sampling technique which leverages complete SAT/CSP solvers to generate high quality samples from hard deterministic spaces. We call the resulting algorithm, GiSS. Unlike Gibbs sampling which yields unweighted samples, GiSS yields weighted samples. Computing the se weights exactly can be computationally expensive and the refore we propose several approximations. We show that our approximate weighting schemes yield consistent estimates and demonstrate experimentally that GiSS is competitive in terms of accuracy with state-of- the -art algorithms such as SampleSearch, MC-SAT and Belief propagation. Copyright © 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

Publication Title

Proceedings of the 27th AAAI Conference on Artificial Intelligence, AAAI 2013

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