Bayesian Conditional Tensor Factorizations for High-Dimensional Classification

doi:10.1080/01621459.2015.1029129

Return

Bayesian Conditional Tensor Factorizations for High-Dimensional Classification

2016-08-18

Yun Yang *

David B. Dunson

DOI：10.1080/01621459.2015.1029129

Original

Save

View PDF

Abstract

En 中文

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors. In settings such as genomics, there can be complex interactions among the predictors. By using a carefully structured Tucker factorization, we define a model that can characterize any conditional probability, while facilitating variable selection and modeling of higher-order interactions. Following a Bayesian approach, we propose a Markov chain Monte Carlo algorithm for posterior computation accommodating uncertainty in the predictors to be included. Under near low-rank assumptions, the posterior distribution for the conditional probability is shown to achieve close to the parametric rate of contraction even in ultra high-dimensional settings. The methods are illustrated using simulation examples and biomedical applications. Supplementary materials for this article are available online.

Keywords:

Classification

Convergence rate

Nonparametric Bayes

Tensor factorization

Ultra high-dimensional

Variable selection

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.