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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| Veröffentlicht in: | International journal of approximate reasoning Jg. 80; S. 52 - 66 |
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| Sprache: | Englisch |
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01.01.2017
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| ISSN: | 0888-613X, 1873-4731 |
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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.
•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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| AbstractList | 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. 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. |
| Author | Cussens, James Angelopoulos, Nicos |
| Author_xml | – sequence: 1 givenname: Nicos orcidid: 0000-0002-7507-9177 surname: Angelopoulos fullname: Angelopoulos, Nicos email: nicos.angelopoulos@sanger.ac.uk organization: Welcome Trust Sanger Institute, Hinxton, CB10 1SA, UK – sequence: 2 givenname: James surname: Cussens fullname: Cussens, James organization: Department of Computer Science, University of York, York, UK |
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| Cites_doi | 10.1007/s10472-009-9133-x 10.1101/gr.098822.109 10.1080/01621459.1998.10473750 10.1017/S1471068410000566 10.1023/A:1010924021315 10.2202/1544-6115.1282 10.1023/A:1007665907178 10.1016/0004-3702(93)90061-F 10.1613/jair.912 10.1007/BF00994016 10.1093/bioinformatics/18.suppl_1.S216 10.1093/nar/28.1.27 10.1038/75556 10.1007/BF01889584 10.1021/ci900046u 10.1007/s10994-015-5488-x |
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| Keywords | Logic programming Bayesian networks Bayesian inference Probabilistic logic programming Classification and regression trees Knowledge representation |
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| SubjectTerms | 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 |
| Title | Distributional logic programming for Bayesian knowledge representation |
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