  Deep neural networks enjoy a powerful representation and have proven
effective in a number of applications. However, recent advances show that deep
neural networks are vulnerable to adversarial attacks incurred by the so-called
adversarial examples. Although the adversarial example is only slightly
different from the input sample, the neural network classifies it as the wrong
class. In order to alleviate this problem, we propose the Deep Minimax
Probability Machine (DeepMPM), which applies MPM to deep neural networks in an
end-to-end fashion. In a worst-case scenario, MPM tries to minimize an upper
bound of misclassification probabilities, considering the global information
(i.e., mean and covariance information of each class). DeepMPM can be more
robust since it learns the worst-case bound on the probability of
misclassification of future data. Experiments on two real-world datasets can
achieve comparable classification performance with CNN, while can be more
robust on adversarial attacks.
