A Uniform Lower Error Bound for Half-Space Learning

Authors:
Andreas Maurer;Massimiliano Pontil
Affiliations:
D-80799, München, Germany;Dept. of Computer Science, University College London, Malet Pl, London, UK WC1E
Venue:
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Year:
2008

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Abstract

We give a lower bound for the error of any unitarily invariant algorithm learning half-spaces against the uniform or related distributions on the unit sphere. The bound is uniform in the choice of the target half-space and has an exponentially decaying deviation probability in the sample. The technique of proof is related to a proof of the Johnson Lindenstrauss Lemma. We argue that, unlike previous lower bounds, our result is well suited to evaluate the benefits of multi-task or transfer learning, or other cases where an expense in the acquisition of domain knowledge has to be justified.