VC-Dimension Based Generalization Bounds for Relational Learning

TL;DR

This paper develops VC-dimension based generalization bounds specifically tailored for relational learning scenarios where data is sampled uniformly without replacement from an unknown larger structure, providing theoretical error bounds.

Contribution

It introduces a novel VC-dimension based bound applicable to relational data under specific sampling assumptions, advancing theoretical understanding in relational learning.

Findings

Derived a VC-dimension based error bound for relational models

Applicable to scenarios with uniform sampling without replacement

Provides theoretical guarantees for relational learning accuracy

Abstract

In many applications of relational learning, the available data can be seen as a sample from a larger relational structure (e.g. we may be given a small fragment from some social network). In this paper we are particularly concerned with scenarios in which we can assume that (i) the domain elements appearing in the given sample have been uniformly sampled without replacement from the (unknown) full domain and (ii) the sample is complete for these domain elements (i.e. it is the full substructure induced by these elements). Within this setting, we study bounds on the error of sufficient statistics of relational models that are estimated on the available data. As our main result, we prove a bound based on a variant of the Vapnik-Chervonenkis dimension which is suitable for relational data.