The VC dimension of partial concept classes via Radon's theorem
Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$). Its VC dimension is defined by shattering sets on which the value $\ast$ is not taken. We study two geometric PCCs in real Banach spaces, both with a margin \(δ>0\): expanded half-spaces, where the grey part is a strip of width at least \(δ\) adjacent to a half-space, and expanded balls, where the grey part is an annulus of width \(δ\) around a unit radius ball. Our main results are dimension-free upper bou...
| Authors | Grigory Ivanov, Attila Jung, Márton Naszódi |
|---|---|
| Primary category | cs.LG |
| Published | 12 July 2026 |
| Last updated at source | 12 July 2026 |
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