Graphbased Generalization Bounds for Learning Binary Relations
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 learningtheoretic arguments. We present a unified, graphbased analysis, which allows us to analyze this dependence using wellknown 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.5348
 Bibcode:
 2013arXiv1302.5348L
 Keywords:

 Computer Science  Machine Learning