A0360
Title: Measuring the impact of the prior in Bayesian nonparametrics via optimal transport
Authors: Marta Catalano - University of Warwick (United Kingdom) [presenting]
Abstract: The Dirichlet process has been pivotal to the development of Bayesian nonparametric, allowing one to learn the law of the observations through closed-form expressions. Still, its learning mechanism is often too simplistic, and many generalizations have been proposed to increase its flexibility, a popular one being the class of normalized completely random measures. A simple yet fundamental matter is investigated: will a different prior actually guarantee a different learning outcome? To this end, a new framework is developed for assessing the merging rate of opinions based on three leading pillars: i) the investigation of identifiability of completely random measures; ii) the measurement of their discrepancy through a novel optimal transport distance; iii) the establishment of general techniques to conduct posterior analyses, unravelling both finite-sample and asymptotic behaviour of the distance as the number of observations grows. The findings provide neat and interpretable insights on the impact of popular Bayesian nonparametric priors, with very mild assumptions on the data-generating process.
