## A Tutorial on Logic-Based Approaches to SRL

author: James Cussens, Department of Computer Science, University of York
published: Sept. 18, 2009,   recorded: July 2009,   views: 365
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# Slides

0:00 Slides A tutorial on logic-based approaches to SRL Overview Making the connections Propositional logic Propositional formulae as zero-one factors Propositional probabilistic models Generalising propositional logic Further examples Weighted clauses Bayesian networks Inference in propositional probabilistic models First-order logic Characteristics of first-order logic Factor representation of universally quantified formulae First-order models Inference in first-order logic First-order probabilistic models (parfactors) Quantifying over random variables What sort of probability distribution is defined? Lifted inference in first-order probabilistic models - 1 Lifted inference in first-order probabilistic models - 2 Quantifying over random variables Lifted inference in first-order probabilistic models - 2 Markov logic parfactors Markov logic distribution What’s the data? First-order probabilistic models (generative) Dynamic probabilistic models The PRISM approach An example "base" probability distribution Defining a "base" distribution in PRISM A joint instantiation determines a logical theory Using a fixed, arbitrary logical theory to extend a base distribution Working with target predicates Computing target probabilities from a PRISM distribution Abduction: A HMM example - 1 Abduction: A HMM example - 2 Abduction: A HMM example - 3 Abduction: A HMM example - 4 Abduction: A HMM example - 5 Computing probabilities by abduction - 1 Computing probabilities by abduction - 2 Computing probabilities by abduction - 3 Computing probabilities by abduction - 4 Computing probabilities by abduction - 5 Computing probabilities by abduction - 6 What’s the data? Bayesian network learning for pedigrees Some genetics The problem Defining a joint probability distribution Pedigree and auxiliary variables Ordered genotype variables Unordered genotype variables An example possible world Penalty for heterozygosity Encoding population frequencies Priors on pedigrees Incorporating evidence An simple example A result Another result An simple example Another result - Questions

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# Description

The relations in Statistical Relational Learning are often expressed using first-order logic, leading to formalisms which combine both logical and probabilistic representations. In this talk I intend to explain the most important consequences of adopting a logical approach to SRL. Defining distributions over 'possible worlds' is a common theme to many such approaches. Two prominent logic-based formalisms - Markov logic networks and PRISM programs - will be used as exemplars. Although the talk is tutorial in nature, I hope to make it interesting to those already familiar with this area!