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From Factorial and Hierarchical HMM to Bayesian Network : A Representation Change Algorithm

Sylvain Gelly 1 Nicolas Bredeche 1 Michèle Sebag 1
1 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : Factorial Hierarchical Hidden Markov Models (FHHMM) provides a powerful way to endow an autonomous mobile robot with efficient map-building and map-navigation behaviors. However, the inference mechanism in FHHMM has seldom been studied. In this paper, we suggest an algorithm that transforms a FHHMM into a Bayesian Network in order to be able to perform inference. As a matter of fact, inference in Bayesian Network is a well-known mechanism and this representation formalism provides a well grounded theoretical background that may help us to achieve our goal. The algorithm we present can handle two problems arising in such a representation change : (1) the cost due to taking into account multiple dependencies between variables (e.g. compute $P(Y|X_1,X_2,...,X_n)$), and (2) the removal of the directed cycles that may be present in the source graph. Finally, we show that our model is able to learn faster than a classical Bayesian network based representation when few (or unreliable) data is available, which is a key feature when it comes to mobile robotics.
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https://hal.inria.fr/inria-00000548
Contributor : Sylvain Gelly <>
Submitted on : Thursday, November 9, 2006 - 4:21:31 PM
Last modification on : Thursday, March 18, 2021 - 12:16:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:16:46 PM

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Sylvain Gelly, Nicolas Bredeche, Michèle Sebag. From Factorial and Hierarchical HMM to Bayesian Network : A Representation Change Algorithm. Symposium on Abstraction, Reformulation and Approximation, Jul 2005, Edinburgh, Scotland, UK. ⟨inria-00000548⟩

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