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New VC dimension bounds for partial concept classes in L_p spaces

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Researchers have extended the concept of VC dimension to partial functions, specifically focusing on geometric partial concept classes (PCCs) in real Banach spaces. They established dimension-free upper bounds for the VC dimension of expanded balls in L_p spaces, which are independent of the ambient dimension and the underlying measure space. These findings build upon prior work in Euclidean spaces and include matching lower bounds and a new Dense Neighborhood Lemma in L_p spaces, utilizing functional analysis techniques and a no-dimensional Radon theorem. AI

IMPACT Extends theoretical understanding of concept classes, potentially impacting generalization bounds in machine learning.

RANK_REASON The item is an academic paper detailing theoretical research in machine learning, specifically on VC dimension. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New VC dimension bounds for partial concept classes in L_p spaces

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The item is an academic paper detailing theoretical research in machine learning, specifically on VC dimension. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Grigory Ivanov, Attila Jung, M\'arton Nasz\'odi ·

    The VC dimension of partial concept classes via Radon's theorem

    arXiv:2607.10751v1 Announce Type: new Abstract: 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 ($f^{-1}(1)$),…

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