From Factorial and Hierarchical HMM to Bayesian Network : A Representation Change Algorithm
Sylvain Gelly, Nicolas Bredeche and Michele Sebag
In: SARA 2005 : Symposium on Abstraction, Reformulation and Approximation, 26-29 Jul 2005, Edinburgh.
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.