An Optimal Sauer Lemma Over $k$-ary Alphabets
The Sauer-Shelah-Perles Lemma is a cornerstone of combinatorics and learning theory, bounding the size of a binary hypothesis class in terms of its Vapnik-Chervonenkis (VC) dimension. For classes of functions over a $k$-ary alphabet, namely the multiclass setting, the Natarajan dimension has long served as an analogue of VC dimension, yet the corresponding Sauer-type bounds are suboptimal for alphabet sizes $k>2$. In this work, we establish a sharp Sauer inequality for multiclass and list prediction. Our bound is expressed in terms of the Daniely--Shalev-Shwartz (DS) dimension, and more generally with its extension, the list-DS dimension -- the combinatorial parameters that characterize m...
| Authors | Steve Hanneke, Qinglin Meng, Shay Moran et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 April 2026 |
| Last updated at source | 14 April 2026 |
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