The Infinite Hierarchical Factor Regression Model

TL;DR

This paper introduces a nonparametric Bayesian hierarchical factor regression model that dynamically infers the number of factors and their relationships, using a sparse Indian Buffet Process and Kingman's coalescent, applied to gene-expression data.

Contribution

It presents a novel hierarchical Bayesian model combining a sparse Indian Buffet Process with Kingman's coalescent for flexible factor analysis and regression.

Findings

Successfully applied to gene-expression data analysis.

Effectively infers the number of factors and their hierarchical relationships.

Demonstrates improved modeling of uncertainty in factor structures.

Abstract

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.