A1476
Title: Tree-embedded Bayesian factor models for multidimensional categorical distributions
Authors: Naoki Awaya - Waseda University (Japan)
Genya Kobayashi - Meiji University (Japan)
Shonosuke Sugasawa - Keio University (Japan)
Keisuke Sasaki - University of Tokyo (Japan) [presenting]
Abstract: Estimating common and heterogeneous structures from multiple data sources via hierarchical models is a central Bayesian inference task, where Bayesian factor models are widely used. A novel Bayesian latent factor model is proposed to parsimoniously describe many observed distributions. Social science applications often involve grouped data, such as regional age or income distributions. Standard mixture models can be inefficient here, as these distributions may lack clear clustering structures. To address this, a tree-based transformation is introduced that embeds distributions into Euclidean space, constructing the factor model there. This transformation allows straightforward extensions of the Bayesian hierarchical model. For instance, spatial dependence is incorporated using a simultaneous autoregressive prior. The model is nonparametric, imposing no strict assumptions on the observed distributions' forms. Numerical experiments with real population data show the model outperforms standard Dirichlet mixture models.
