A0302
Title: Matrix-variate priors for flexible mixture modelling of grouped data
Authors: Beatrice Franzolini - Bocconi University (Italy)
Andrea Cremaschi - IE University (Spain) [presenting]
Abstract: In the last two decades, the Bayesian nonparametric literature witnessed significant progress in the study of 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. A notable example is 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. A novel class of dependent priors is proposed for mixture modelling based on finite-dimensional matrix-variate distributions for the weights of the mixture. Specifically, the matrix-variate Dirichlet distribution is employed as a 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 while inducing dependence and appropriate borrowing of information across groups. The 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.
