A fast Bayesian method that seamlessly fuses classification and hypothesis testing via discriminant analysis is developed. Building upon the original discriminant analysis classifier, modelling components are added to identify discriminative variables. A combination of cake priors and a novel form of variational Bayes we call reverse collapsed variational Bayes gives rise to variable selection that can be directly posed as a multiple hypothesis testing approach using likelihood ratio statistics. Some theoretical arguments are presented showing that Chernoff-consistency (asymptotically zero type I and type II error) is maintained across all hypotheses. We apply our method on some publicly available genomics datasets and show that our method performs well in practice for its computational cost. An R package VaDA has also been made available on Github.

中文翻译：

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变量选择的变分判别分析

开发了一种快速的贝叶斯方法，该方法通过判别分析将分类和假设检验无缝地融合在一起。在原始判别分析分类器的基础上，添加建模组件以标识判别变量。蛋糕先验与新颖形式的变分贝叶斯的组合（我们称为反向折叠变分贝叶斯）引起了变量选择，可以使用似然比统计将其直接提出为多重假设检验方法。提出了一些理论论证，表明在所有假设中都保持了切尔诺夫一致性（渐近为零的I型和II型误差）。我们将我们的方法应用于一些可公开获得的基因组数据集，并表明我们的方法在计算成本方面在实践中表现良好。一个[R包VaDA也已在Github上提供。