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Distributional logic programming for Bayesian knowledge representation

Angelopoulos, N; Cussens, J; (2017) Distributional logic programming for Bayesian knowledge representation. International Journal of Approximate Reasoning , 80 pp. 52-66. 10.1016/j.ijar.2016.08.004. Green open access

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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.

Type: Article
Title: Distributional logic programming for Bayesian knowledge representation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.ijar.2016.08.004
Publisher version: https://doi.org/10.1016/j.ijar.2016.08.004
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Probabilistic logic programming, Bayesian inference, Bayesian networks, Classification and regression trees, Knowledge representation, Logic programming
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Medical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10057341
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