Info Gap Bayesian Classification

Optimal decision methods and most notably the Bayesian decision are sensitive to uncertainty in the statistics of the patterns to be classified. Errors in the associated probabilities and distributions would degrade the performance of these methods. We present here a robust-satisficing decision-rule whose robustness to uncertainty in the priors is maximized given a performance demand. We apply the method to a two-class medical classification problem. We show that the robust-satisficing decision-rule is more robust to uncertainty in the priors than the optimal Bayesian decision-rule at sub-optimal performance levels. We present 4 propositions which characterize the robust-satisficing classifier. In addition we demonstrate the capabilities of this method when applied to uncertainty in the conditional probability density functions.