Coresets for polytope distance

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Coresets for polytope distance
Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance between two polytopes, Perceptrons, and soft- as well as hard-margin Support Vector Machines (SVM). We prove asymptotically matching upper and lower bounds on the size of coresets, stating that -coresets of size (1 + o(1))E∗ / do always exist as → 0, and that this is best possible. The crucial quantity E∗ is what we call the excentricity of a polytope, or a pair of polytopes. Additionally, we prove linear convergence speed of Gilbert’s algorithm, one of the earliest known approximation algorithms for polytope distance, and generalize both the algorithm and the proof to the two polytope case. Interestingly, our coreset bounds also imply that we can for the first time prove matching upper and lower bounds for the sparsity of Perceptron and SVM solutions. Categories and Subject Descriptors F.2.2 [Analy...
Bernd Gärtner, Martin Jaggi
Added 28 May 2010
Updated 28 May 2010
Type Conference
Year 2009
Authors Bernd Gärtner, Martin Jaggi
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