Title: New insights on Bayesian graphs and neural networks from distributional properties
Authors: Julyan Arbel - Inria (France) [presenting]
Florence Forbes - INRIA (France)
Mariia Vladimirova - Inria (France)
Hongliang Lu - Inria (France)
Abstract: Ongoing work on Bayesian modeling of (1) graphs and (2) neural networks is considered. Part (1) is devoted to Bayesian nonparametric modeling of data structured as a graph. In such a setting, the usual assumption of exchangeability does not hold. We rely on a Potts component in the prior in order to account for graph dependencies. Such a prior induces a distribution on partitions akin to the celebrated Chinese restaurant process. We derive distributional properties which highlight the Potts contribution to the clustering mechanism. Part (2) focuses on distributional results of Bayesian neural networks. We derive some new non-asymptotic results highlighting that the deeper the network layer, the heavier-tailed the unit distribution.