nips nips2000 nips2000-44 nips2000-44-reference knowledge-graph by maker-knowledge-mining
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Author: Shai Ben-David, Hans-Ulrich Simon
Abstract: We consider the existence of efficient algorithms for learning the class of half-spaces in ~n in the agnostic learning model (Le., making no prior assumptions on the example-generating distribution). The resulting combinatorial problem - finding the best agreement half-space over an input sample - is NP hard to approximate to within some constant factor. We suggest a way to circumvent this theoretical bound by introducing a new measure of success for such algorithms. An algorithm is IL-margin successful if the agreement ratio of the half-space it outputs is as good as that of any half-space once training points that are inside the IL-margins of its separating hyper-plane are disregarded. We prove crisp computational complexity results with respect to this success measure: On one hand, for every positive IL, there exist efficient (poly-time) IL-margin successful learning algorithms. On the other hand, we prove that unless P=NP, there is no algorithm that runs in time polynomial in the sample size and in 1/ IL that is IL-margin successful for all IL> O. 1