Distributional logic programming for Bayesian knowledge representation

Nicos Angelopoulos*, James Cussens

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)

Abstract

We present a formalism for combining logic programming and its flavour of nondeterminism with probabilistic reasoning. In particular, we focus on representing prior knowledge for Bayesian inference. Distributional logic programming (Dlp), is considered in the context of a class of generative probabilistic languages. A characterisation based on probabilistic paths which can play a central role in clausal probabilistic reasoning is presented. We illustrate how the characterisation can be utilised to clarify derived distributions with regards to mixing the logical and probabilistic constituents of generative languages. We use this operational characterisation to define a class of programs that exhibit probabilistic determinism. We show how Dlp can be used to define generative priors over statistical model spaces. For example, a single program can generate all possible Bayesian networks having N nodes while at the same time it defines a prior that penalises networks with large families. Two classes of statistical models are considered: Bayesian networks and classification and regression trees. Finally we discuss: (1) a Metropolis–Hastings algorithm that can take advantage of the defined priors and the probabilistic choice points in the prior programs and (2) its application to real-world machine learning tasks.
Original languageEnglish
Pages (from-to)52-66
Number of pages15
JournalInternational Journal of Approximate Reasoning
Volume80
Early online date17 Aug 2016
DOIs
Publication statusPublished - 1 Jan 2017

Bibliographical note

© 2016 Elsevier Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

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