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arXiv · 1812.03648

Variational Nonparametric Discriminant Analysis

Weichang Yu·Lamiae Azizi·John T. Ormerod
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Abstract

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A novel Bayesian nonparametric discriminant analysis model that performs both variable selection and classification within a seamless framework is proposed. P{\'o}lya tree priors are assigned to the unknown group-conditional distributions to account for their uncertainty, and allow prior beliefs about the distributions to be incorporated simply as hyperparameters. The adoption of collapsed variational Bayes inference in combination with a chain of functional approximations led to an algorithm with low computational cost. The resultant decision rules carry heuristic interpretations and are related to an existing two-sample Bayesian nonparametric hypothesis test. By an application to some simulated and publicly available real datasets, the proposed method exhibits good performance when compared to current state-of-the-art approaches.

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Weichang Yu, Lamiae Azizi, John T. Ormerod. 2018-12-10. Variational Nonparametric Discriminant Analysis. https://arxiv.org/abs/1812.03648

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