A Close Look to Margin Complexity and Related Parameters

Michael Kallweit, Hans Ulrich Simon
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:437-456, 2011.

Abstract

Concept classes can canonically be represented by sign-matrices, i.e., by matrices with entries 1 and −1. The question whether a sign-matrix (concept class) A can be learned by a machine that performs large margin classification is closely related to the “margin complexity” associated with A. We consider several variants of margin complexity, reveal how they are related to each other, and we reveal how they are related to other notions of learning-theoretic relevance like SQ-dimension, CSQ-dimension, and the Forster bound.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-kallweit11a, title = {A Close Look to Margin Complexity and Related Parameters}, author = {Kallweit, Michael and Simon, Hans Ulrich}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {437--456}, year = {2011}, editor = {Kakade, Sham M. and von Luxburg, Ulrike}, volume = {19}, series = {Proceedings of Machine Learning Research}, address = {Budapest, Hungary}, month = {09--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v19/kallweit11a/kallweit11a.pdf}, url = {https://proceedings.mlr.press/v19/kallweit11a.html}, abstract = {Concept classes can canonically be represented by sign-matrices, i.e., by matrices with entries $1$ and $-1$. The question whether a sign-matrix (concept class) $A$ can be learned by a machine that performs large margin classification is closely related to the “margin complexity” associated with $A$. We consider several variants of margin complexity, reveal how they are related to each other, and we reveal how they are related to other notions of learning-theoretic relevance like SQ-dimension, CSQ-dimension, and the Forster bound.} }
Endnote
%0 Conference Paper %T A Close Look to Margin Complexity and Related Parameters %A Michael Kallweit %A Hans Ulrich Simon %B Proceedings of the 24th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2011 %E Sham M. Kakade %E Ulrike von Luxburg %F pmlr-v19-kallweit11a %I PMLR %P 437--456 %U https://proceedings.mlr.press/v19/kallweit11a.html %V 19 %X Concept classes can canonically be represented by sign-matrices, i.e., by matrices with entries $1$ and $-1$. The question whether a sign-matrix (concept class) $A$ can be learned by a machine that performs large margin classification is closely related to the “margin complexity” associated with $A$. We consider several variants of margin complexity, reveal how they are related to each other, and we reveal how they are related to other notions of learning-theoretic relevance like SQ-dimension, CSQ-dimension, and the Forster bound.
RIS
TY - CPAPER TI - A Close Look to Margin Complexity and Related Parameters AU - Michael Kallweit AU - Hans Ulrich Simon BT - Proceedings of the 24th Annual Conference on Learning Theory DA - 2011/12/21 ED - Sham M. Kakade ED - Ulrike von Luxburg ID - pmlr-v19-kallweit11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 437 EP - 456 L1 - http://proceedings.mlr.press/v19/kallweit11a/kallweit11a.pdf UR - https://proceedings.mlr.press/v19/kallweit11a.html AB - Concept classes can canonically be represented by sign-matrices, i.e., by matrices with entries $1$ and $-1$. The question whether a sign-matrix (concept class) $A$ can be learned by a machine that performs large margin classification is closely related to the “margin complexity” associated with $A$. We consider several variants of margin complexity, reveal how they are related to each other, and we reveal how they are related to other notions of learning-theoretic relevance like SQ-dimension, CSQ-dimension, and the Forster bound. ER -
APA
Kallweit, M. & Simon, H.U.. (2011). A Close Look to Margin Complexity and Related Parameters. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:437-456 Available from https://proceedings.mlr.press/v19/kallweit11a.html.

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