Variational nonparametric discriminant analysis

Weichang Yu, Lamiae Azizi and John T. Ormerod

Computational Statistics & Data Analysis, 2020, vol. 142, issue C

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. Pólya 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.

Keywords: Variational inference; Bayesian nonparametrics; Pólya trees; Classification; Variable selection; High dimensional statistics (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301641

DOI: 10.1016/j.csda.2019.106817

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