Zoom link - Filippo Ascolani - November 8

[All About That Bayes]

Dear all,

a gentle reminder that tomorrow's session is a mirror session hosted at INRIA Grenoble. The talk will be broadcasted on zoom : https://univ-grenoble-alpes-fr.zoom.us/j/93236504120?pwd=WngySU9FSzJGYVE3b253Ympubk9kdz09

Have a good evening.

The organisers

Filippo Ascolani (Bocconi University) - Clustering consistency with Dirichlet process mixtures

Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration parameter of the underlying Dirichlet process. Previous findings in the literature suggest that Dirichlet process mixtures are typically not consistent for the number of clusters if the concentration parameter is held fixed and data come from a finite mixture. Here we show that consistency for the number of clusters can be achieved if the concentration parameter is adapted in a fully Bayesian way, as commonly done in practice. Our results are derived for data coming from a class of finite mixtures, with mild assumptions on the prior for the concentration parameter and for a variety of choices of likelihood kernels for the mixture.

Joint work with Antonio Lijoi, Giovanni Rebaudo, and Giacomo Zanelli.

Reference: https://arxiv.org/abs/2205.12924 (Biometrika, forthcoming)

Webpage: https://filippoascolani.github.io/