There is a tradeoff between generalization capability and computational overhead in multi-class leaing. We propose a generative probabilistic multi-class classifi er, considering both the generalization capability and the leaing/prediction rate. We show that the classifi er has a max-margin property. Thus, prediction on future unseen data can nearly achieve the same performance as in the training stage. In addition, local variables are eliminated, which greatly simplifi es the optimization problem. By convex and probabilistic analysis, an e?cient online leaing algorithm is developed. The algorithm aggregates rather than averages dualities, which is different from the classical situations. Empirical results indicate that our method has a good generalization capability and coverage rate.