Habilitation à Diriger des Recherches

Eric Fabre

Irisa - 14 juin 2007

Bayesian Networks of Dynamic Systems

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Bayesian networks, or Markov random fields, are well known statistical models that describe the interactions of large sets of random variables. Their interest is to represent graphically the structure of variable interactions, from which statistical inference algorithms can be designed.

In this work, we explore different ways of introducing time in such systems. The idea is to replace cliques of random variables by (possibly stochastic) dynamic systems. So the values of a variable may change in time. The models we obtain are networks of interacting automata, extremely convenient to represent complex distributed softwares or systems. The counterpart of statistical inference for these models consists in guessing what happened in the system given sequences of observations collected on the different components.

To do so, we borrow to computer scientists their techniques to represent runs of concurrent systems, in different semantics. We show that runs of these distributed dynamic systems enjoy a nice factorization property, just like the probability distribution in a Bayesian network factorizes (Hammersley-Clifford theorem). The resemblence is such that inference algorithms for Bayesian networks can adapted to distributed dynamic systems. We actually provide a common algebraic framework that encompasses both situations. This bridge between graphical models and concurrency theory allows us to translate, for example, turbo algorithms into distributed on-line inference strategies, and to study their properties

We will illustrate the interest of this approach with applications to the distributed failure diagnosis in telecommunication networks.

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