Generalized Bayesian Infinite Factor Models

• Activity Number: 40
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Kassie Fronczyk*+
• Companies: Rice University
• Keywords: Bayesian nonparametrics ; sparsity ; Indian buffet process ; Markov chain Monte Carlo ; factor analysis

Abstract

Experiments generating high dimensional data are becoming more prevalent throughout the literature, with examples ranging from genomics and biology to imaging. A widely used approach to analyze this type of data is factor analysis, where the aim is to explain observations with a linear projection of independent hidden factors. Given a number of latent factors and loadings are random variables, traditional models assume some sort of isotropic or diagonal error covariance structure, gaining insight for correlations only across the rows of the data. We extend this idea to a more general setting, where interest lies in correlations of the rows and columns of the data and the number of factors is treated as an unknown parameter. We explore a fully Bayesian approach to obtain inference on the latent factors and loadings, as well as for the latent dimension of the data.