Bayesian Conditional Tensor Factorizations for High-Dimensional Classification.

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Yang, Y; Dunson, DB

Published Date

  • January 2016

Published In

Volume / Issue

  • 111 / 514

Start / End Page

  • 656 - 669

PubMed ID

  • 31983790

Pubmed Central ID

  • 31983790

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2015.1029129

Language

  • eng