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Bayesian Conditional Tensor Factorizations for High-Dimensional Classification
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 sparsity 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
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