Approximation algorithms for minimizing empirical error by axis-parallel hyperplanes

Authors:
Tapio Elomaa;Jussi Kujala;Juho Rousu
Affiliations:
Institute of Software Systems, Tampere University of Technology;Institute of Software Systems, Tampere University of Technology;Department of Computer Science, Royal Holloway University of London
Venue:
ECML'05 Proceedings of the 16th European conference on Machine Learning
Year:
2005

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Abstract

Many learning situations involve separation of labeled training instances by hyperplanes. Consistent separation is of theoretical interest, but the real goal is rather to minimize the number of errors using a bounded number of hyperplanes. Exact minimization of empirical error in a high-dimensional grid induced into the feature space by axis-parallel hyperplanes is NP-hard. We develop two approximation schemes with performance guarantees, a greedy set covering scheme for producing a consistently labeled grid, and integer programming rounding scheme for finding the minimum error grid with bounded number of hyperplanes.