Inference in Multilayer Networks via Large Deviation Bounds

Arguably one of the most important types of information processing is the capacity for probabilistic reasoning. The properties of undirectedproDabilistic models represented as symmetric networks have been studied extensively using methods from statistical mechanics (Hertz et aI, 1991). Detailed analyses of these models are possible by exploiting averaging phenomena that occur in the thermodynamic limit of large networks. In this paper, we analyze the limit of large, multilayer networks for probabilistic models represented as directed acyclic graphs. These models are known as Bayesian networks (Pearl, 1988; Neal, 1992), and they have different probabilistic semantics than symmetric neural networks (such as Hopfield models or Boltzmann machines). We show that the intractability of exact inference in multilayer Bayesian networks Inference in Multilayer Networks via Large Deviation Bounds 261 does not preclude their effective use. Our work builds on earlier studies of variational methods (Jordan et aI, 1997).