On the Consistency of Optimal Bayesian Feature Selection in the Presence of Correlations
This work provides theoretical guarantees for OBFS in biomarker discovery, which is incremental but important for justifying its use and understanding asymptotic behavior in related algorithms.
The authors proved that Gaussian optimal Bayesian feature selection (OBFS) is strongly consistent under mild conditions and provided convergence rates for key posteriors, establishing what features are selected asymptotically and characterizing convergence rates for different feature types.
Optimal Bayesian feature selection (OBFS) is a multivariate supervised screening method designed from the ground up for biomarker discovery. In this work, we prove that Gaussian OBFS is strongly consistent under mild conditions, and provide rates of convergence for key posteriors in the framework. These results are of enormous importance, since they identify precisely what features are selected by OBFS asymptotically, characterize the relative rates of convergence for posteriors on different types of features, provide conditions that guarantee convergence, justify the use of OBFS when its internal assumptions are invalid, and set the stage for understanding the asymptotic behavior of other algorithms based on the OBFS framework.