TY - UNPB
T1 - Fat-Shattering Dimension of k-fold Aggregations
AU - Kontorovich, Aryeh
AU - Attias, Idan
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2021/10/10
Y1 - 2021/10/10
N2 - We provide improved estimates on the fat-shattering dimension of the k-fold maximum of real-valued function classes. The latter consists of all ways of choosing k functions, one from each of the k classes, and computing their pointwise maximum. The bound is stated in terms of the fat-shattering dimensions of the component classes. For linear and affine function classes, we provide a considerably sharper upper bound and a matching lower bound, achieving, in particular, an optimal dependence on k. Along the way, we point out and correct a number of erroneous claims in the literature.
AB - We provide improved estimates on the fat-shattering dimension of the k-fold maximum of real-valued function classes. The latter consists of all ways of choosing k functions, one from each of the k classes, and computing their pointwise maximum. The bound is stated in terms of the fat-shattering dimensions of the component classes. For linear and affine function classes, we provide a considerably sharper upper bound and a matching lower bound, achieving, in particular, an optimal dependence on k. Along the way, we point out and correct a number of erroneous claims in the literature.
U2 - 10.48550/arXiv.2110.04763
DO - 10.48550/arXiv.2110.04763
M3 - Preprint
BT - Fat-Shattering Dimension of k-fold Aggregations
ER -