Minimax Regret Classifier for Imprecise Class Distributions

The design of a minimum risk classifier based on data usually stems from the stationarity assumption that the conditions during training and test are the same: the misclassification costs assumed during training must be in agreement with real costs, and the same statistical process must have generated both training and test data. Unfortunately, in real world applications, these assumptions may not hold. This paper deals with the problem of training a classifier when prior probabilities cannot be reliably induced from training data. Some strategies based on optimizing the worst possible case (conventional minimax) have been proposed previously in the literature, but they may achieve a robust classification at the expense of a severe performance degradation. In this paper we propose a minimax regret (minimax deviation) approach, that seeks to minimize the maximum deviation from the performance of the optimal risk classifier. A neural-based minimax regret classifier for general multi-class decision problems is presented. Experimental results show its robustness and the advantages in relation to other approaches.