On the Consistency of Optimal Bayesian Feature Selection in the Presence of Correlations

Optimal Bayesian feature selection (OBFS) is a multivariat e supervised screening method designed from the ground up for bioma rker discovery. In this work, we prove that Gaussian OBFS is strongly consisten t under mild conditions, and provide rates of convergence for key posteriors i n the framework. These results are of enormous importance, since they identify pre cisely what features are selected by OBFS asymptotically, characterize the relativ e rates of convergence for posteriors on different types of features, provide condi tions that guarantee convergence, justify the use of OBFS when its internal assum ptions are invalid, and set the stage for understanding the asymptotic behavior of other algorithms based on the OBFS framework.