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Irisa - 14 juin
Bayesian Networks of Dynamic Systems
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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