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Structure Approximation of Most Probable Explanations in Bayesian Networks

  • Johan Kwisthout
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7958)

Abstract

Typically, when one discusses approximation algorithms for (NP-hard) problems (like Traveling Salesperson, Vertex Cover, Knapsack), one refers to algorithms that return a solution whose value is (at least ideally) close to optimal; e.g., a tour with almost minimal length, a vertex cover of size just above minimal, or a collection of objects that has close to maximal value. In contrast, one might also be interested in approximation algorithms that return solutions that resemble the optimal solutions, i.e., whose structure is akin to the optimal solution, like a tour that is almost similar to the optimal tour, a vertex cover that differs in only a few vertices from the optimal cover, or a collection that is similar to the optimal collection. In this paper, we discuss structure-approximation of the problem of finding the most probable explanation of observations in Bayesian networks, i.e., finding a joint value assignment that looks like the most probable one, rather than has an almost as high value. We show that it is NP-hard to obtain the value of just a single variable of the most probable explanation. However, when partial orders on the values of the variables are available, we can improve on these results.

Keywords

Approximation Algorithm Polynomial Time Bayesian Network Vertex Cover Probable Explanation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Johan Kwisthout
    • 1
  1. 1.Donders Institute for Brain, Cognition and BehaviourRadboud University NijmegenNijmegenThe Netherlands

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