Marta Catalano is PhD candidate in the Department of Decision Sciences at Bocconi University, under the supervision of Antonio Lijoi and Igor Prünster. Before moving to Milan, she graduated in Mathematics at University of Rome La Sapienza. She is an elected board member of the young Italian Statistical Society (y-SIS) and coordinates a biweekly internal seminar series at the Bocconi Institute for Data Science and Analytics (BIDSA). Her research targets Bayesian nonparametric models for complex data structures, with a particular focus on statistical applications of optimal transport and completely random measures.
Talk: Measuring dependence in the Wasserstein distance for Bayesian nonparametric models
A link to this Zoom talk will be sent to the Stats Seminar list serv
Abstract: Bayesian nonparametric models are a prominent tool for performing flexible inference with a natural quantification of uncertainty. The main ingredient are discrete random measures, whose law acts as prior distribution for infinite-dimensional parameters in the models and, combined with the data, provides their posterior distribution. Recent works use dependent random measures to perform simultaneous inference across multiple samples. The borrowing of strength across different samples is regulated by the dependence structure of the random measures, with complete dependence corresponding to maximal share of information and fully exchangeable observations. For a substantial prior elicitation it is crucial to quantify the dependence in terms of the hyperparameters of the models. State-of-the-art methods partially achieve this through the expression of the pairwise linear correlation. In this talk we propose the first non-linear measure of dependence for random measures. Starting from the two samples case, dependence is characterized in terms of distance from exchangeability through a suitable metric on vectors of random measures based on the Wasserstein distance. This intuitive definition extends naturally to an arbitrary number of samples and it is analytically tractable on noteworthy models in the literature.