Distributional logic programming for Bayesian knowledge representation

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 probabi...

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Bibliographic Details
Published in:International journal of approximate reasoning Vol. 80; pp. 52 - 66
Main Authors: Angelopoulos, Nicos, Cussens, James
Format: Journal Article
Language:English
Published: Elsevier Inc 01.01.2017
Subjects:
Bayesian analysis
Bayesian inference
Bayesian networks
Classification and regression trees
Knowledge representation
Logic programming
Mathematical models
Probabilistic logic programming
Probabilistic methods
Probability theory
Reasoning
Statistical analysis
Logic programming
Bayesian networks
Bayesian inference
Probabilistic logic programming
Classification and regression trees
Knowledge representation
ISSN:0888-613X, 1873-4731
Online Access:Get full text
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Summary: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. •Knowledge representation for Bayesian machine learning.•Probabilistic logic programming for modelling prior over model structure.•Implementation of a system for likelihood based learning.•Effect of prior information to proposal model structures.•Proposal free MCMC simulations.
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ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2016.08.004