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arXiv · 1805.09719

Learning convex polyhedra with margin

Lee-Ad Gottlieb·Eran Kaufman·Aryeh Kontorovich·Gabriel Nivasch
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Abstract

We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polyhedron as an intersection of about $t \log t$ halfspaces with constant-size margins in time polynomial in $t$ (where $t$ is the number of halfspaces forming an optimal polyhedron). We also identify distinct generalizations of the notion of margin from hyperplanes to polyhedra and investigate how they relate geometrically; this result may have ramifications beyond the learning setting.

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BibTeXRIS

Lee-Ad Gottlieb, Eran Kaufman, Aryeh Kontorovich, Gabriel Nivasch. 2018-05-24. Learning convex polyhedra with margin. https://arxiv.org/abs/1805.09719

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