High-arity Sample Compression

TL;DR

This paper explores high-arity sample compression schemes in learning theory, establishing that their existence implies high-arity PAC learnability, thus advancing understanding of learning in product spaces.

Contribution

It introduces a high-arity variant of sample compression schemes and proves their connection to high-arity PAC learnability.

Findings

High-arity sample compression schemes imply high-arity PAC learnability.

The work extends learning theory concepts to product spaces.

Provides theoretical foundations for high-arity learning models.

Abstract

Recently, a series of works have started studying variations of concepts from learning theory for product spaces, which can be collected under the name high-arity learning theory. In this work, we consider a high-arity variant of sample compression schemes and we prove that the existence of a high-arity sample compression scheme of non-trivial quality implies high-arity PAC learnability.