Statistics and Computational Methods Seminar Series - 2024/25

Speaker: Beatrice Franzolini (Bocconi University)

Title: Extending Stochastic Block models to Multiplex Networks via Conditional Partial Exchangeability

Abstract:

In recent years, there has been significant progress in developing models for dependent partitions that extend beyond both exchangeability and partial exchangeability within the Bayesian nonparametric literature. These models may incorporate temporal dynamics or separate exchangeability assumptions into random partition frameworks. This talk will provide an overview of these recent advancements, with a particular focus on the probabilistic properties of conditional partial exchangeability (CPE), a unifying framework for symmetry assumptions in dependent partitions of the same objects. CPE differs from traditional partial exchangeability due to its conditional nature and its requirement for marginal invariance. Together, these conditions ensure local dependence among partitions.

Building on this theoretical framework, we have developed a hierarchically extended stochastic block model for modeling multiplex networks. Stochastic block models are commonly used to identify groups of nodes with similar connectivity patterns within networks. However, their applicability is limited when dealing with modern structured network data, such as multiplex networks, where multiple types of edges exist among the same set of nodes.

In contrast, the hierarchically extended stochastic block model is designed to account for dependencies across different types of connection patterns in multiplex networks. It effectively infers both connection-specific and global block structures while preserving node identity across layers.

This presentation draws primarily on two works: one with Prof. Maria De Iorio and another with Dr. Valentina Ghidini and Prof. Daniele Durante