6 papers
Measures of Dependence based on Wasserstein distances
Marta Catalano, Hugo Lavenant
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlatio…
Measuring Partial Exchangeability with Reproducing Kernel Hilbert Spaces
Marta Catalano, Hugo Lavenant, Francesco Mascari
In Bayesian multilevel models, the data are structured in interconnected groups, and their posteriors borrow information from one another due to prior dependence between latent par…
Hierarchical Random Measures without Tables
Marta Catalano, Claudio Del Sole
The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly…
Hierarchical Integral Probability Metrics: A distance on random probability measures with low sample complexity
Marta Catalano, Hugo Lavenant
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities se…
Merging Rate of Opinions via Optimal Transport on Random Measures
Marta Catalano, Hugo Lavenant
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the ra…
A Wasserstein index of dependence for random measures
Marta Catalano, Hugo Lavenant, Antonio Lijoi +1
Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optim…