Bayesian Conditional Tensor Factorizations for High-Dimensional Classification. Issue 514 (2nd April 2016)

• Record Type: Journal Article
• Authors: Yang, Yun; Dunson, David B.
• Is Part Of: Journal of the American Statistical Association. Volume 111:Issue 514(2016)
• Page Start: 656
• Page End: 669
• Publication Date: 2016-04-02
• Subjects: Classification -- Convergence rate -- Nonparametric Bayes -- Tensor factorization -- Ultra high-dimensional -- Variable selection; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2015.1029129
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: 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.