Tensor Factorization Transformation Priors for Density Regression

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jared Murray*+
• Keywords: Density Regression ; Density Estimation ; Tensor Factorization ; B-Splines ; Latent Variable ; Bayesian Nonparametrics

Abstract

Characterizing how an entire probability distribution changes with covariates is an important and challenging generalization of mean and quantile regression methods. Existing nonparametric Bayesian models for this task are large, hard to understand and difficult to center at reasonable parametric alter- natives. These problems are especially pronounced with categorical covariates; models with even a few categorical variables are difficult to specify and fit with existing methods without making restrictive assumptions about the nature and depth of interactions.

I present an alternative continuous (uncountable) mixture model for densities based on smooth transformations of latent uniform random variables. In the regression setting there is a transformation for each cell of the contingency table; a hierarchical tensor factorization prior allows partial pooling of these transformations, inducing flexible shrinkage of entire densities across cells.