High-arity PAC learning via exchangeability
Leonardo N. Coregliano Maryanthe Malliaris
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.