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Abstract:
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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. Recent works use dependent random measures to perform simultaneous inference across multiple samples. The borrowing of strength across samples is regulated by the dependence 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 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 Wasserstein type of distance on vectors of random measures. This intuitive definition extends naturally to an arbitrary number of samples and it is analytically tractable on noteworthy models in the literature.
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