A Robust Probability Classifier Based on the Modifiedχ2-Distance

We propose a robust probability classifier model to addressclassification problems with data uncertainty. A class-conditional probabilitydistributional set is constructed based on the modified -distance. Based on a “linear combination assumption” for the posterior class-conditional probabilities,we consider a classification criterion using the weighted sum of theposterior probabilities. An optimal robust minimax classifier is defined as theone with the minimal worst-case absolute error loss function value over allpossible distributions belonging to the constructed distributional set. Basedon the conic duality theorem, we show that the resulted optimization problemcan be reformulated into a second order cone programming problemwhich can be efficiently solved by interior algorithms. The robustness of theproposed model can avoid the “overlearning” phenomenon on training setsand thus keep a comparable accuracy on test sets. Numerical experimentsvalidate the effectiveness of the proposed model and further show that it alsoprovides promising results on multiple classification problems.