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In biclassification problems with many features, it is important to select a few of them, to ensure fairness and explainability in the original data space. We control the feature number (to be specified by the user) with a hard cardinality (zero-norm) constraint and solve the resulting difficult optimization problem by a conic decomposition approach. This exhibits promising scalability properties while maintaining both explainability and good predictive performance. From an optimization point of view, our approach is competitive with previous similar attempts employing mixed-binary linear optimization technology. These however use different techniques like bi-level formulations, surrogates for the zero-norm, or convex relaxationsIn biclassification problems with many features, it is important to select a few of them, to ensure fairness and explainability in the original data space. We control the feature number (to be specified by the user) with a hard cardinality (zero-norm) constraint and solve the resulting difficult optimization problem by a conic decomposition approach. This exhibits promising scalability properties while maintaining both explainability and good predictive performance. From an optimization point of view, our approach is competitive with previous similar attempts employing mixed-binary linear optimization technology. These however use different techniques like bi-level formulations, surrogates for the zero-norm, or convex relaxations, see for instance [1,2,3,4], and not all of them always exert strict control on the number of features., and not all of them always exert strict control on the number of features.

Biclassification, zero norm, conic optimization