Read a finite-class generalization bound

Problem

A finite hypothesis class has $\lvert\mathcal{H}\rvert=100$ and $n=1000$ independent examples. Using

$\varepsilon=\sqrt{\frac{\log\left(2\lvert\mathcal{H}\rvert/\delta\right)}{2n}}$

with $\delta=0.05$ , compute $\varepsilon$ and explain what the simultaneous bound says.

Reveal answer or reference solution

$\varepsilon=\sqrt{\frac{\log(4000)}{2000}}\approx 0.0644.$

With probability at least $0.95$ , every hypothesis in $\mathcal{H}$ has empirical and population error differing by at most this amount under the bound's assumptions.

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