Minimax strategies for training classifiers under unknown priors

Most supervised learning algorithms are based on the assumption that the training data set reflects the underlying statistical model of the real data. However, this stationarity assumption is not always satisfied in practice: quite frequently, class prior probabilities are not in accordance with the class proportions in the training data set. The minimax approach is based on selecting the classifier that minimize the error probability under the worst case conditions. We propose a two-step learning algorithm to train a neural network in order to estimate the minimax classifier that is robust to changes in the class priors. During the first step, posterior probabilities based on training data priors are estimated. During the second step, class priors are modified in order to minimize a cost function that is asymptotically equivalent to the worst-case error rate. This procedure is illustrated on a softmax-based neural network. Several experimental results show the advantages of the proposed method with respect to other approaches.