Abstract
There is a growing interest in the logical representation of both probabilistic and deterministic dependencies. While Gibbs sampling is a widely-used method for estimating probabilities, it is known to give poor results in the presence of determinism. In this paper, we consider acyclic Horn logic, a small, but significant fragment of first-order logic and show that Markov chains constructed with Gibbs sampling remain ergodic with deterministic dependencies specified in this fragment. Thus, there is a new subclass of Gibbs sampling procedures known to approximate the correct probabilities and expected to be useful for lots of applications.
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Gries, O. (2011). Gibbs Sampling with Deterministic Dependencies. In: Sombattheera, C., Agarwal, A., Udgata, S.K., Lavangnananda, K. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2011. Lecture Notes in Computer Science(), vol 7080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25725-4_37
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DOI: https://doi.org/10.1007/978-3-642-25725-4_37
Publisher Name: Springer, Berlin, Heidelberg
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