A Mutual Information Based Ensemble Method to Estimate Bayes Error

Determining the performance bounds possible with a particular clas-siier or data set is often of great importance in pattern recognition applications. A previously introduced method for Bayes error estimation based on combining multiple classiiers outperforms more traditional estimates of this error in many instances. The accuracy of this estimate, however, relies on the correlation among the classiiers, a quantity that may be diicult to quantify precisely. Addressing this issue, we explore improvements to the ensemble based estimates of the Bayes error by considering information theo-retic issues. More precisely, we use mutual information to determine a \similarity" measure between trained classiiers. This approach provides a more reliable similarity measure than error correlation, and leads to more accurate bounds on classiication error. Application to an artiicial problem with known Bayes error rate and a real world problem involving underwater acoustic data demonstrates the accuracy of this method.