Title:
Matrix-variate priors for flexible mixture modelling of grouped data

Co-authors:
B. Franzolini

Abstract:
In the last two decades, significant progress has been made in the Bayesian nonparametric literature to introduce and study novel dependent prior distributions beyond standard univariate species sampling processes. These dependent priors are developed
under partial exchangeability assumptions and capture dependencies in heterogeneous data settings with grouped data. Notable efforts have focused on nonparametric hierarchical processes, such as the celebrated Hierarchical Dirichlet Process. However, with a few exceptions, less attention has been given to finite-dimensional dependent mixture models and dependent mixtures with a random number of components. In this work, we propose a highly tractable class of dependent priors for mixture modelling, based on finite-dimensional matrix-variate distributions for the weights of the mixture. Specifically, we employ the matrix-variate Dirichlet distribution as joint prior for the weights of the multi-group mixture. The distributional properties of the matrix-variate Dirichlet distribution ensure standard assumptions for the weights of each mixture (i.e., positivity and sum-to-one property), while inducing dependence and appropriate borrowing of information across groups. Our approach goes beyond standard univariate weights, allowing for varying levels of description of the data features and accommodating group-specific kernels. This enables flexible modelling of different data types and various ways in which the information can be shared across groups. The proposed model is widely applicable and yields interpretable results. We develop a tailored MCMC algorithm for posterior sampling and demonstrate the proposed approach on both simulated and real-data examples.

Keywords:
matrix-variate Dirichlet, multi-group mixture models, dependent weight mixtures

Link Google Meet: 
https://meet.google.com/jjm-xtiz-djd