Open Access
December 2020 Theory of Optimal Bayesian Feature Filtering
Ali Foroughi pour, Lori A. Dalton
Bayesian Anal. 15(4): 1169-1197 (December 2020). DOI: 10.1214/19-BA1182


Optimal Bayesian feature filtering (OBF) is a supervised screening method designed for biomarker discovery. In this article, we prove two major theoretical properties of OBF. First, optimal Bayesian feature selection under a general family of Bayesian models reduces to filtering if and only if the underlying Bayesian model assumes all features are mutually independent. Therefore, OBF is optimal if and only if one assumes all features are mutually independent, and OBF is the only filter method that is optimal under at least one model in the general Bayesian framework. Second, OBF under independent Gaussian models is consistent under very mild conditions, including cases where the data is non-Gaussian with correlated features. This result provides conditions where OBF is guaranteed to identify the correct feature set given enough data, and it justifies the use of OBF in non-design settings where its assumptions are invalid.


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Ali Foroughi pour. Lori A. Dalton. "Theory of Optimal Bayesian Feature Filtering." Bayesian Anal. 15 (4) 1169 - 1197, December 2020.


Published: December 2020
First available in Project Euclid: 30 October 2019

Digital Object Identifier: 10.1214/19-BA1182

Primary: 62C10 , 62F07 , 62F15 , 92C37

Keywords: Bayesian decision theory , biomarker discovery , Variable selection

Vol.15 • No. 4 • December 2020
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