 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-4/30j/c/solution

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

The exponential loss is

ϕ (z) = e^{- z}

. For a score

f : X \to R

R_{ϕ} (f) = E [e^{- Y f (X)}], R_{ϕ} (f) = \frac{1}{n} \sum_{i = 1}^{n} e^{- Y_{i} f (X_{i})} .

B (x_{1 : n}) = {(h (x_{1}), \dots, h (x_{n})) : h \in B},

R (B (x_{1 : n})) = \frac{1}{n} E_{σ} h \in B sup i = 1 \sum n σ_{i} h (x_{i}),

where the

σ_{i}

are independent uniform random signs.

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