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High-dimensional data is common in multiple areas, such as health care andgenomics, where the number of features can be tens of thousands. In suchscenarios, the large number of features often leads to inefficient learning.Constraint generation methods have recently enabled efficient learning ofL1-regularized support vector machines (SVMs). In this paper, we leverage suchmethods to obtain an efficient learning algorithm for the recently proposedminimax risk classifiers (MRCs). The proposed iterative algorithm also providesa sequence of worst-case error probabilities and performs feature selection.Experiments on multiple high-dimensional datasets show that the proposedalgorithm is efficient in high-dimensional scenarios. In addition, theworst-case error probability provides useful information about the classifierperformance, and the features selected by the algorithm are competitive withthe state-of-the-art.

Efficient Learning of Minimax Risk Classifiers in High Dimensions