Abstract: Bayesian factor models represent a very popular tool in analysis of high-dimensional datasets. The cumbersome task of determining the number of factors has in recent years been addressed in literature by employing nonparametric models for the automatic inference on the number of factors. Some latest works introduced division of the dataset into clusters, allowingthe number of factors differ in different clusters, with automatic inference on both clusters and cluster-specific number of factors.
However, to our knowledge, factors are mostly assumed to be normally distributed. In reality, this assumption may prove to be too restrictive. Here, the automatic inference on the number of clusters and factors in the dataset is extended to a non-Gaussian case. We relax the assumption of normality by employing a Laplace prior on factors. For the inference on the number of clusters and cluster-specific factors, we follow the recent literature and employ the dynamic mixture of finite mixtures with the beta-negative-binomial prior on the number of components combined with a shrinkage prior on a cluster-specific number of factors. Two types of shrinkagepriors are considered: the multiplicative gamma process prior and the the cumulative shrinkage process, based on a sequence of spike-and-slab-distributions. The models are tested both on simulated data sets as well as on a Eurozone countries inflation rates data set.
Presentation slides