High-arity PAC learning via exchangeability
Machine Learning
2024-09-18 v3 Logic
Statistics Theory
Statistics Theory
Abstract
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. Our main theorems establish a high-arity (agnostic) version of the fundamental theorem of statistical learning.
Cite
@article{arxiv.2402.14294,
title = {High-arity PAC learning via exchangeability},
author = {Leonardo N. Coregliano and Maryanthe Malliaris},
journal= {arXiv preprint arXiv:2402.14294},
year = {2024}
}
Comments
151 pages, 1 figure. (Minor changes: this version changes the definition of flexibility (3.17 and 4.14) to a weaker one to ensure that the 0/1-loss is flexible, fixing an imprecision in Lemma 3.19; see Footnote 34 in the manuscript for details.)