Variational Nonparametric Discriminant Analysis Article Swipe

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Nonparametric statistics Prior probability Hyperparameter Linear discriminant analysis Machine learning Computer science Bayesian probability Artificial intelligence Bayes' theorem Inference Feature selection Model selection Selection (genetic algorithm) Mathematics Pattern recognition (psychology) Statistics

Weichang Yu , Lamiae Azizi , John T. Ormerod ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1812.03648 · OA: W2905304044

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{ó}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.