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On the Consistency of Optimal Bayesian Feature Selection in the Presence of Correlations
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.
Theory of Optimal Bayesian Feature Filtering
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.
Optimal Clustering under Uncertainty
Herein, we derive an optimal robust clusterer by first finding an effective random point process that incorporates all randomness within its own probabilistic structure and from which a Bayes clusterer can be derived that provides an optimal robust clusterer relative to the uncertainty.
