On the Interaction Effects Between Prediction and Clustering

TL;DR

This paper investigates how interaction effects between clustering and prediction algorithms can bias cross-validation estimates, providing theoretical insights and scalable correction methods validated on benchmark datasets.

Contribution

It offers the first theoretical characterization of interaction effects between clustering and prediction, and develops scalable methods to correct bias in out-of-cluster loss estimation.

Findings

Expected out-of-cluster loss decays rapidly with minor clustering errors.

Traditional cross-validation exhibits significant bias in this setting.

Scaling techniques effectively correct bias and improve estimation.

Abstract

Machine learning systems increasingly depend on pipelines of multiple algorithms to provide high quality and well structured predictions. This paper argues interaction effects between clustering and prediction (e.g. classification, regression) algorithms can cause subtle adverse behaviors during cross-validation that may not be initially apparent. In particular, we focus on the problem of estimating the out-of-cluster (OOC) prediction loss given an approximate clustering with probabilistic error rate $p_0$. Traditional cross-validation techniques exhibit significant empirical bias in this setting, and the few attempts to estimate and correct for these effects are intractable on larger datasets. Further, no previous work has been able to characterize the conditions under which these empirical effects occur, and if they do, what properties they have. We precisely answer these questions by providing theoretical properties which hold in various settings, and prove that expected out-of-cluster loss behavior rapidly decays with even minor clustering errors. Fortunately, we are able to leverage these same properties to construct hypothesis tests and scalable estimators necessary for correcting the problem. Empirical results on benchmark datasets validate our theoretical results and demonstrate how scaling techniques provide solutions to new classes of problems.