Bayesian Conditional Tensor Factorizations for High-Dimensional Classification

Yun Yang and David B. Dunson

Journal of the American Statistical Association, 2016, vol. 111, issue 514, 656-669

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.

Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1080/01621459.2015.1029129

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