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.

翻译：我们用利昂语正式证明(PAC)可能大致正确(PAC)了解决策立木的概念类别。 机器学习理论的这一经典结果对简单的分类师来说是建立在错误概率的界限上。 尽管这种证据在纸面上看起来很简单,但在完全正式进行时会出现分析和测量理论的微妙之处。 我们的证据结构将学习功能的决定性特性与可衡量性和概率分析的证据分开。 我们的证据结构化是为了将学习功能的确定性与可衡量性的证据和概率分析区分开来。