We develop a theory of high-arity PAC learning, which is statistical learning in the presence of "structured correlation". In this theory, hypotheses are either graphs, hypergraphs or, more generally, structures in finite relational languages, and i.i.d. sampling is replaced by sampling an induced substructure, producing an exchangeable distribution. We prove a high-arity version of the fundamental theorem of statistical learning by characterizing high-arity (agnostic) PAC learnability in terms of finiteness of a purely combinatorial dimension and in terms of an appropriate version of uniform convergence.

翻译：我们发展了高元PAC学习理论，这是一种在“结构化相关性”存在下的统计学习理论。在该理论中，假设要么是图、超图，更一般地，是有限关系语言中的结构，而独立同分布采样被替换为采样诱导子结构，从而产生可交换分布。我们通过用纯组合维度的有限性和适当形式的一致收敛性来刻画高元（不可知）PAC可学习性，证明了统计学习基本定理的高元版本。