Graph-based Generalization Bounds for Learning Binary Relations

TL;DR

This paper develops graph-based theoretical bounds on how well binary relations learned from subsampled pairs generalize, using Rademacher complexity and stability, with guarantees under random subsampling.

Contribution

It introduces a unified graph-based analysis framework for dependent pairwise data, deriving new generalization bounds for binary relation learning.

Findings

Bounds depend on the subsampling process.

Under random subsampling, guarantees of ilde{O}(1/√n) convergence.

Analysis handles dependence via graph identities.

Abstract

We investigate the generalizability of learned binary relations: functions that map pairs of instances to a logical indicator. This problem has application in numerous areas of machine learning, such as ranking, entity resolution and link prediction. Our learning framework incorporates an example labeler that, given a sequence $X$ of $n$ instances and a desired training size $m$, subsamples $m$ pairs from $X \times X$ without replacement. The challenge in analyzing this learning scenario is that pairwise combinations of random variables are inherently dependent, which prevents us from using traditional learning-theoretic arguments. We present a unified, graph-based analysis, which allows us to analyze this dependence using well-known graph identities. We are then able to bound the generalization error of learned binary relations using Rademacher complexity and algorithmic stability. The rate of uniform convergence is partially determined by the labeler's subsampling process. We thus examine how various assumptions about subsampling affect generalization; under a natural random subsampling process, our bounds guarantee $\tilde{O}(1/\sqrt{n})$ uniform convergence.