Using histograms to better answer queries to probabilistic logic programs

Matthias Broecheler*, Gerardo I. Simari, V. S. Subrahmanian

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Probabilistic logic programs (PLPs) define a set of probability distribution functions (PDFs) over the set of all Herbrand interpretations of the underlying logical language. When answering a query Q, a lower and upper bound on Q is obtained by optimizing (min and max) an objective function subject to a set of linear constraints whose solutions are the PDFs mentioned above. A common critique not only of PLPs but many probabilistic logics is that the difference between the upper bound and lower bound is large, thus often providing very little useful information in the query answer. In this paper, we provide a new method to answer probabilistic queries that tries to come up with a histogram that "maps" the probability that the objective function will have a value in a given interval, subject to the above linear constraints. This allows the system to return to the user a histogram where he can directly "see" what the most likely probability range for his query will be. We prove that computing these histograms is #P-hard, and show that computing these histograms is closely related to polyhedral volume computation. We show how existing randomized algorithms for volume computation can be adapted to the computation of such histograms. A prototype experimental implementation is discussed.

Original languageEnglish (US)
Title of host publicationLogic Programming - 25th International Conference, ICLP 2009, Proceedings
Pages40-54
Number of pages15
DOIs
StatePublished - 2009
Externally publishedYes
Event25th International Conference on Logic Programming, ICLP 2009 - Pasadena, CA, United States
Duration: Jul 14 2009Jul 17 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5649 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Conference on Logic Programming, ICLP 2009
Country/TerritoryUnited States
CityPasadena, CA
Period7/14/097/17/09

Keywords

  • Imprecise Probabilities
  • Probabilistic Logic Programming

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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