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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/31j/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 31J / c / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

x \mapsto x^{T} β

form a real vector space of dimension

p

. Hence the VC dimension of a vector space gives

VC (H_{F_{1}}) \leq p .

Applying the Sauer-Shelah lemma and then the Sauer-Shelah growth bound,

s (H_{F_{1}}, n) \leq \sum_{j = 0}^{p} (j n) \leq (n + 1)^{p} .

This is the growth bound for homogeneous linear classifiers.

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