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 modifiedχ2-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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.