A Tutorial on Logic-Based Approaches to SRL
author:
James Cussens,
Department of Computer Science, University of York
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!
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| Slides | |
| 0:00 | A tutorial on logic-based approaches to SRL |
| 0:38 | Overview |
| 1:50 | Making the connections |
| 2:16 | Propositional logic |
| 2:19 | Propositional formulae as zero-one factors |
| 4:55 | Propositional probabilistic models |
| 5:07 | Generalising propositional logic |
| 6:56 | Further examples |
| 7:51 | Weighted clauses |
| 10:11 | Bayesian networks |
| 10:51 | Inference in propositional probabilistic models |
| 12:30 | First-order logic |
| 12:43 | Characteristics of first-order logic |
| 14:23 | Factor representation of universally quantified formulae |
| 15:14 | First-order models |
| 16:32 | Inference in first-order logic |
| 18:05 | First-order probabilistic models (parfactors) |
| 18:51 | Quantifying over random variables |
| 21:17 | What sort of probability distribution is defined? |
| 25:42 | Lifted inference in first-order probabilistic models - 1 |
| 27:09 | Lifted inference in first-order probabilistic models - 2 |
| 27:24 | Quantifying over random variables |
| 27:47 | Lifted inference in first-order probabilistic models - 2 |
| 28:40 | Markov logic parfactors |
| 29:52 | Markov logic distribution |
| 31:26 | What’s the data? |
| 32:41 | First-order probabilistic models (generative) |
| 33:04 | Dynamic probabilistic models |
| 34:57 | The PRISM approach |
| 35:44 | An example "base" probability distribution |
| 37:03 | Defining a "base" distribution in PRISM |
| 37:36 | A joint instantiation determines a logical theory |
| 38:33 | Using a fixed, arbitrary logical theory to extend a base distribution |
| 40:37 | Working with target predicates |
| 41:46 | Computing target probabilities from a PRISM distribution |
| 42:36 | Abduction: A HMM example - 1 |
| 43:25 | Abduction: A HMM example - 2 |
| 43:30 | Abduction: A HMM example - 3 |
| 43:31 | Abduction: A HMM example - 4 |
| 43:32 | Abduction: A HMM example - 5 |
| 43:44 | Computing probabilities by abduction - 1 |
| 43:46 | Computing probabilities by abduction - 2 |
| 44:48 | Computing probabilities by abduction - 3 |
| 44:49 | Computing probabilities by abduction - 4 |
| 44:50 | Computing probabilities by abduction - 5 |
| 44:51 | Computing probabilities by abduction - 6 |
| 45:37 | What’s the data? |
| 46:29 | Bayesian network learning for pedigrees |
| 49:35 | Some genetics |
| 50:45 | The problem |
| 51:59 | Defining a joint probability distribution |
| 53:12 | Pedigree and auxiliary variables |
| 54:07 | Ordered genotype variables |
| 54:54 | Unordered genotype variables |
| 55:10 | An example possible world |
| 55:27 | Penalty for heterozygosity |
| 56:03 | Encoding population frequencies |
| 56:30 | Priors on pedigrees |
| 57:03 | Incorporating evidence |
| 57:27 | An simple example |
| 57:48 | A result |
| 58:33 | Another result |
| 58:38 | An simple example |
| 58:43 | Another result |
| 59:17 | - Questions |
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