Title: Transport-based measure of dependence for Bayesian nonparametric models
Authors: Antonio Lijoi - Bocconi University (Italy)
Igor Pruenster - Bocconi University (Italy)
Marta Catalano - University of Torino (Italy) [presenting]
Abstract: Dependent random measures are a prominent tool for performing Bayesian nonparametric inference across multiple populations. 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. Dependence is characterized in terms of distance from exchangeability through a suitable transport metric 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.