Supervised classification via minimax probabilistic transformations
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One of the most common and studied problem in machine learning is classification. While conventional algorithms for supervised classification rely on the determination of a function from features to labels, we propose a different approach based on the estimation of a probabilistic transformation from features to labels. Indeed, we determine a conditional probability distribution of the labels given the features and then features are classified as labels following such distribution. In order to compute the conditional distribution, we follow a robust minimax approach, minimizing the worst-case expectation of the 0-1 loss. By doing so, we find the probabilistic transformation which achieves the minimum risk against an uncertainty set consistent with the training data. We show numerical results obtained by an implementation in python of this method and we compare its performance with state of the art techniques.
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