Reproduce “Uniform convergence at optimal rate and scale” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Noga Alon, Steve Hanneke, Shay Moran, Tom Waknine
The authors establish a worst-case bound for estimating every function’s expectation from one random sample. Uniform convergence means the same sample works for all functions; fat-shattering dimension measures complexity at resolution gamma. With dimension d at that scale, O((d+log(1/delta))/epsilon^2) samples guarantee error gamma+epsilon with confidence 1-delta. A matching lower bound applies to a constructed worst-case class, not every class.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.