Bayesian Conditional Tensor Factorizations for High-Dimensional Classification

Yun Yang, David B. Dunson

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)656-669
Number of pages14
JournalJournal of the American Statistical Association
Issue number514
StatePublished - Apr 2 2016
Externally publishedYes


  • Classification
  • Convergence rate
  • Nonparametric Bayes
  • Tensor factorization
  • Ultra high-dimensional
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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