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Markov Logic in Infinite Domains

Authors: Pedro Domingos and Parag Singla

Published in: Dagstuhl Seminar Proceedings, Volume 7161, Probabilistic, Logical and Relational Learning - A Further Synthesis (2008)

Abstract

Markov logic combines logic and probability by attaching weights to first-order formulas, and viewing them as templates for features of Markov networks. Unfortunately, in its original formulation it does not have the full power of first-order logic, because it applies only to finite domains. Recently, we have extended Markov logic to infinite domains, by casting it in the framework of Gibbs measures. In this talk I will summarize our main results to date, including sufficient conditions for the existence and uniqueness of a Gibbs measure consistent with an infinite MLN, and properties of the set of consistent measures in the non-unique case. (Many important phenomena, like phase transitions, are modeled by non-unique MLNs.) Under the conditions for existence, we have extended to infinite domains the result in Richardson and Domingos (2006) that first-order logic is the limiting case of Markov logic when all weights tend to infinity. I will also discuss some fundamental limitations of Herbrand interpretations (and representations based on them) for probabilistic modeling of infinite domains, and how to get around them. Finally, I will discuss some of the surprising insights for learning and inference in large finite domains that result from considering the infinite limit.

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Pedro Domingos and Parag Singla. Markov Logic in Infinite Domains. In Probabilistic, Logical and Relational Learning - A Further Synthesis. Dagstuhl Seminar Proceedings, Volume 7161, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{domingos_et_al:DagSemProc.07161.6,
  author =	{Domingos, Pedro and Singla, Parag},
  title =	{{Markov Logic in Infinite Domains}},
  booktitle =	{Probabilistic, Logical and Relational Learning - A Further Synthesis},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7161},
  editor =	{Luc de Raedt and Thomas Dietterich and Lise Getoor and Kristian Kersting and Stephen H. Muggleton},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07161.6},
  URN =		{urn:nbn:de:0030-drops-13811},
  doi =		{10.4230/DagSemProc.07161.6},
  annote =	{Keywords: Markov logic networks, Gibbs measures, first-order logic, infinite probabilistic models, Markov networks}
}

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1 Search Results for "Domingos, Pedro"

Markov Logic in Infinite Domains

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