# Rounding Methods for Discrete Linear Classification

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Yann Chevaleyre,
Frédéerick Koriche,
Jean-daniel Zucker
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Proceedings of the 30th International Conference on Machine Learning, PMLR 28(1):651-659, 2013.

#### Abstract

Learning discrete linear functions is a notoriously difficult challenge. In this paper, the learning task is cast as combinatorial optimization problem: given a set of positive and negative feature vectors in the Euclidean space, the goal is to find a discrete linear function that minimizes the cumulative hinge loss of this training set. Since this problem is NP-hard, we propose two simple rounding algorithms that discretize the fractional solution of the problem. Generalization bounds are derived for two important classes of binary-weighted linear functions, by establishing the Rademacher complexity of these classes and proving approximation bounds for rounding methods. These methods are compared on both synthetic and real-world data.

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