On Wednesday, March 27th, 2024, the seminar series hosted a talk by Dr James Ng, Assistant Professor at the School of Computer Science and Statistics in Trinity College Dublin. James talked about a generalized Bayesian approach to distribution-on-distribution regression. Details for the talk are below.
Title
A Generalized Bayesian Approach to Distribution-on-Distribution Regression
Abstract
In recent years, there has been growing interest in distribution-on-distribution regression, a regression problem where both covariates and responses are represented as probability distributions. Despite various methodologies proposed to address this challenge, a notable absence has been a Bayesian approach, which offers benefits by allowing for the integration of prior knowledge and providing a formal means of quantifying uncertainty. However, a major challenge in employing a Bayesian approach lies in the complexity of fully specifying the data generating process. To overcome this obstacle, we adopt a generalized Bayesian approach and investigate the contraction rates of the resulting generalized (Gibbs) posterior distributions.