License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07161.6
URN: urn:nbn:de:0030-drops-13811
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1381/
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Domingos, Pedro ;
Singla, Parag
Markov Logic in Infinite Domains
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.
BibTeX - Entry
@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.dagstuhl.de/opus/volltexte/2008/1381},
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}
}
Keywords: |
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Markov logic networks, Gibbs measures, first-order logic, infinite probabilistic models, Markov networks |
Collection: |
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07161 - Probabilistic, Logical and Relational Learning - A Further Synthesis |
Issue Date: |
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2008 |
Date of publication: |
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06.03.2008 |