A Formal Proof of PAC Learnability for Decision Stumps
arXiv:1911.00385 · doi:10.1145/3437992.3439917
Abstract
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoretic subtleties arise when carrying it out fully formally. Our proof is structured so as to separate reasoning about deterministic properties of a learning function from proofs of measurability and analysis of probabilities.
13 pages, appeared in Certified Programs and Proofs (CPP) 2021