Application of Sparse Exchangeable Graphs to Infinite Latent Feature Modeling

• Activity Number: 553 - Bayesian Nonparametrics
• Type: Invited
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Zacharie Naulet*
• Companies: University of Toronto

Abstract

Bayesian non-parametric feature allocation schemes are built on top of a prior distribution over infinite binary matrices; typically using using the Beta-Binomial process or its combinatorial structure the Indian buffet Process. Recent work in statistical network modelling has introduced sparse exchangeable graph distributions: a large class of new probability distributions over random graphs with an infinite number of vertices. A bipartite graph drawn from one of these distributions may be viewed as defining an infinite feature allocation by identifying one partition with features and the other partition with the objects to which features are assigned. As such, sparse exchangeable graph distributions define Bayesian non-parametric priors for feature allocations. We show that this framework naturally includes previous models, including the Indian buffet process, and we demonstrate that the model class can accommodate a range of behaviours outside the purview of traditional Bayesian non-parametrics. We also show how sampling schemes for these distributions can be used to make inferences in latent feature allocation tasks.