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"Probabilistic Logic Learning" - Tutorial

Content

This is a tutorial on probabilistic-logical models (PLMs). PLMs integrate a traditional probabilistic model with some first-order logical or relational representation language. For instance, Bayesian networks or hidden Markov models are selected and upgraded by incorporating entity-relationship (ER) models, Datalog, or Prolog. More precisely, we will focus on probabilistic logic learning (PLL), i.e. learning in PLMs. The main goal of the tutorial is to provide an introduction to and a survey of approaches to probabilistic logic learning. The outline and the content of the tutorial are adopted from
L. De Raedt, K. Kersting. Probabilistic Logic Learning. In ACM-SIGKDD Explorations, special issue on Multi-Relational Data Mining, Vol. 5(1), pp. 31-48, July 2003, [link]
and will be:

1) Introduction to PLL
(20 min.):
  • objectives of PLL
  • a motivating application
2) Foundations of PLL
( 30 min.)
  • Halpern's Type I vs. Type II approaches[Hal89] and
  • model-theoretical vs. proof-theoretical approaches;
  • basic concepts from logic programming and traditional probabilistic models.
3) Frameworks of PLL
(100 min.)		 Coherent picture of PLL approaches:
  • proof-theoretical: David Poole's probabilistic Horn abduction (PHA) [Poo93], Muggleton's stochastic logic programs (SLPs) [Mug96,Cus00], Sato's PRISM [Sat95,SK01]. Relationship to statistical work on ``Highly-Structured Stochastic Systems''.
  • model-theoretic: Ngo and Haddawy's probabilistic-logic programs (PLPs) [NH97], Koller et al.'s probabilistic relational models (PRMs) [FGKP99,Pfe00,Get01], Kersting and De Raedt's Bayesian logic programs (BLPs) [KD01a,KD01b], Getoor's statistical relational models (SRMs) [Get01].
  • intermediate: Anderson et al.'s and Kersting et al.'s relational Markov Models [ADWeld02,KRKD03].
4) Applications of PLL
(30 min.) 		Web mining; bioinformatics applications, Bayesian modelling

PLMs can roughly be classified as model-theoretic and proof-theoretic. Model-theoretic PLMs determine probabilities in terms of possible worlds, whereas proof-theoretic PLMs specifies probabilities by means of possible proofs with respect to a given goal. This is not a hard dichotomy, most approaches contain elements of both these methods. Furthermore, the frameworks addressed in the ``proof-theoretical'' and the ``model-theoretical'' blocks of part 3 integrate probabilistic models with very expressive relational representations or even logic programs. This, however, comes at a computational cost. The ``intermediate'' approaches can be viewed as downgrading one of the more expressive ones presented before such that (1) they are closely related to the underlying representations, (2) they are -- in principle -- more efficient, and (3) the learning algorithms for the underlying representations can almost directly be applied.

It is also planned to establish a PLL playground. The playground will be a web page where (plain) implementations of e.g. PCFGs, PRMs, SRMs, SLPs, BLPs, PRISMs etc. will be provided so that people can improve their understanding of PLLs in practice.