Optimal mean-square-error calibration of classifier error estimators under Bayesian models

A recently proposed Bayesian modeling framework for classification facilitates both the analysis and optimization of error estimation performance. The Bayesian error estimator is then defined to have optimal mean-square error performance, but in many situations closed-form representations are unavailable and approximations may not be feasible. To address this, we present a method to optimally calibrate arbitrary error estimators for minimum mean-square error performance within a supposed Bayesian framework. Assuming a fixed sample size, classification rule and error estimation rule, as well as a fixed Bayesian model, the calibration is done by first computing a calibration function that maps error estimates to their optimally calibrated values off-line. Once found, this calibration function may be easily applied to error estimates on the fly whenever the assumptions apply. We demonstrate that calibrated error estimators offer significant improvement in performance relative to classical error estimators under Bayesian models with both linear and non-linear classification rules.