Uniform convergence at optimal rate and scale
Uniform convergence asks how many random samples suffice for empirical averages to approximate expectations simultaneously over an entire class of functions. It is a central concept in probability and a foundation of statistical learning. For binary-valued classes, the Vapnik--Chervonenkis theorem characterizes uniform convergence by finiteness of the VC dimension. For dimension $d$, the sharp worst-case sample complexity for additive error $\varepsilon$ is of order $d/\varepsilon^2$. For real-valued functions, the analogous combinatorial parameter is the fat-shattering dimension, which depends on an approximation scale $γ$. The challenge is to achieve error $γ+\varepsilon$ with order $d/...
| Authors | Noga Alon, Steve Hanneke, Shay Moran et al. |
|---|---|
| Primary category | cs.LG |
| Published | 17 October 2026 |
| Last updated at source | 17 October 2026 |
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