Fat-shattering dimension of k-fold maxima.

Aryeh Kontorovich, Idan Attias

Research output: Working paper/PreprintPreprint


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.
Original languageEnglish
StatePublished - 10 Oct 2021


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