Search problems in the domain of multiplication: Case study on robust anomaly detection using markov chains

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Abstract

Most work in heuristic search focused on path finding problems in which the cost of a path in the state space is the sum of its edges’ weights. This paper addresses a different class of path finding problems in which the cost of a path is the product of its weights. We present reductions from different classes of multiplicative path finding problems to suitable classes of additive path finding problems. As a case study, we consider the problem of finding least and most probable paths in a Markov Chain, where path cost corresponds to the probability of traversing it. The importance of this problem is demonstrated in an anomaly detection application for cyberspace security. Three novel anomaly detection metrics for Markov Chains are presented, where computing these metrics require finding least and most probable paths. The underlying Markov Chain is dynamically changing, and so fast methods for computing least and most probable paths are needed. We propose such methods based on the proposed reductions and using heuristic search algorithms.

Original languageEnglish
Title of host publicationProceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015
EditorsLevi Lelis, Roni Stern
PublisherAAAI press
Pages70-77
Number of pages8
ISBN (Electronic)9781577357322
StatePublished - 1 Jan 2015
Event8th Annual Symposium on Combinatorial Search, SoCS 2015 - Ein Gedi, Israel
Duration: 11 Jun 201513 Jun 2015

Publication series

NameProceedings of the 8th Annual Symposium on Combinatorial Search, SoCS 2015
Volume2015-January

Conference

Conference8th Annual Symposium on Combinatorial Search, SoCS 2015
Country/TerritoryIsrael
CityEin Gedi
Period11/06/1513/06/15

Keywords

  • Anomaly detection
  • Markov Chains
  • Multiplication domain search
  • Network intrusion detection
  • Search space monotonicity

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