Generalization in Adaptive Data Analysis and Holdout Reuse

TL;DR

This paper introduces a practical method for reusing holdout sets in adaptive data analysis to prevent overfitting, extending differential privacy techniques and proposing a unifying framework based on max-information.

Contribution

It presents a new algorithm for adaptive holdout validation, broadens the application of differential privacy in data analysis, and introduces the concept of approximate max-information for data reuse guarantees.

Findings

The proposed algorithm effectively prevents overfitting in adaptive hypothesis testing.

Differential privacy-based methods can be applied to broader adaptive analysis scenarios.

Approximate max-information unifies different approaches to data reuse in adaptive settings.

Abstract

Overfitting is the bane of data analysts, even when data are plentiful. Formal approaches to understanding this problem focus on statistical inference and generalization of individual analysis procedures. Yet the practice of data analysis is an inherently interactive and adaptive process: new analyses and hypotheses are proposed after seeing the results of previous ones, parameters are tuned on the basis of obtained results, and datasets are shared and reused. An investigation of this gap has recently been initiated by the authors in (Dwork et al., 2014), where we focused on the problem of estimating expectations of adaptively chosen functions. In this paper, we give a simple and practical method for reusing a holdout (or testing) set to validate the accuracy of hypotheses produced by a learning algorithm operating on a training set. Reusing a holdout set adaptively multiple times can easily lead to overfitting to the holdout set itself. We give an algorithm that enables the validation of a large number of adaptively chosen hypotheses, while provably avoiding overfitting. We illustrate the advantages of our algorithm over the standard use of the holdout set via a simple synthetic experiment. We also formalize and address the general problem of data reuse in adaptive data analysis. We show how the differential-privacy based approach given in (Dwork et al., 2014) is applicable much more broadly to adaptive data analysis. We then show that a simple approach based on description length can also be used to give guarantees of statistical validity in adaptive settings. Finally, we demonstrate that these incomparable approaches can be unified via the notion of approximate max-information that we introduce.