Bayesian graphs and networks

This talk focuses on ongoing work on Bayesian modeling of (1) graphs and (2) neural networks. 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 some preliminary results on distributional properties which highlight the Potts contribution to the clustering mechanism. Part (2) focuses on distributional results of Bayesian neural networks. We start by reviewing some known results, such as the Gaussian or alpha-stable process wide limit. We then derive some new non-asymptotic results highlighting that the deeper the network layer, the heavier-tailed the unit distribution.

 

Joint work with Hongliang Lü, Florence Forbes and Mariia Vladimirova (Inria Grenoble – Rhône-Alpes, Laboratoire Jean Kuntzmann).