A Robust Probability Classifier Based on the Modified χ2-Distance

We propose a robust probability classifier model to address classification problems with data uncertainty. A class-conditional probability distributional set is constructed based on the modified chi(2)-distance. Based on a "linear combination assumption" for the posterior class-conditional probabilities, we consider a classification criterion using the weighted sum of the posterior probabilities. An optimal robust minimax classifier is defined as the one with the minimal worst-case absolute error loss function value over all possible distributions belonging to the constructed distributional set. Based on the conic duality theorem, we show that the resulted optimization problem can be reformulated into a second order cone programming problem which can be efficiently solved by interior algorithms. The robustness of the proposed model can avoid the "overlearning" phenomenon on training sets and thus keep a comparable accuracy on test sets. Numerical experiments validate the effectiveness of the proposed model and further show that it also provides promising results on multiple classification problems.