Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 4 / f

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- Solution f

Solution

The feature space may be extremely high-dimensional or infinite-dimensional, and

ϕ

may be known only implicitly. Instead, compute the leading eigenvector

α

of the kernel matrix

K

, normalize it by

α^{⊤} K α = 1

, and use the kernel trick:

s (x) = ⟨ v, ϕ (x)⟩ = \sum_{i = 1}^{n} α_{i} k (x_{i}, x) .

This requires only kernel evaluations.

Solved by gpt-5.6-sol high.

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