Reconstruction of Markov random fields from samples: Some observations and algorithms

Guy Bresler, Elchanan Mossel, Allan Sly

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

52 Scopus citations

Abstract

Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random fields. We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on n nodes and maximum degree d given observations. We show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using Θ(d log n) samples which is optimal up to a multiplicative constant. Our results seem to be the first results for general models that guarantee that the generating model is reconstructed. Furthermore, we provide an explicit O(dnd+2log n) running time bound. In cases where the measure on the graph has correlation decay, the running time is O(n2log n) for all fixed d. In the full-length version we also discuss the effect of observing noisy samples. There we show that as long as the noise level is low, our algorithm is effective. On the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions. Finally, we briefly show that in some cases, models with hidden nodes can also be recovered.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings
Pages343-356
Number of pages14
DOIs
StatePublished - 2008
Event11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008 - Boston, MA, United States
Duration: Aug 25 2008Aug 27 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5171 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008
CountryUnited States
CityBoston, MA
Period8/25/088/27/08

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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