Fat-Shattering of Affine Functions

Authors:
Don Hush;Clint Scovel
Affiliations:
Modeling, Algorithms and Informatics Group, CCS-3, Mail Stop B265, Los Alamos National Laboratory, Los Alamos, NM 87545, USA (e-mail: dhush@lanl.gov);Modeling, Algorithms and Informatics Group, CCS-3, Mail Stop B265, Los Alamos National Laboratory, Los Alamos, NM 87545, USA (e-mail: jcs@lanl.gov)
Venue:
Combinatorics, Probability and Computing
Year:
2004

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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.