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Fat-Shattering of Affine Functions

Published online by Cambridge University Press:  28 April 2004

DON HUSH  and
CLINT SCOVEL
DON HUSH
Affiliation:
Modeling, Algorithms and Informatics Group, CCS-3, Mail Stop B265, Los Alamos National Laboratory, Los Alamos, NM 87545, USA (e-mail: dhush@lanl.gov)
CLINT SCOVEL
Affiliation:
Modeling, Algorithms and Informatics Group, CCS-3, Mail Stop B265, Los Alamos National Laboratory, Los Alamos, NM 87545, USA (e-mail: jcs@lanl.gov)
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Abstract

We compute the fat-shattering function and the level fat-shattering function for important classes of affine functions. We observe that the level fat-shattering function and the fat-shattering function are identical for these classes. In addition we observe that the notion that adding the constant term to linear functions increases the dimension by at most 1 is incorrect for fat-shattering and level fat-shattering.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 3 , May 2004 , pp. 353 - 360
Copyright
2004 Cambridge University Press

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