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A0483
Title: Measuring dependence in the Wasserstein distance for Bayesian nonparametric models Authors:  Antonio Lijoi - Bocconi University (Italy)
Igor Pruenster - Bocconi University (Italy)
Marta Catalano - University of Warwick (United Kingdom) [presenting]
Abstract: Bayesian nonparametric models are a prominent tool for performing flexible inference with a natural quantification of uncertainty. The main ingredient is 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 the 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. 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.