How much does your data exploration overfit? Controlling bias via information usage

TL;DR

This paper introduces an information-theoretic framework to quantify and control bias in data exploration, providing bounds and insights into how adaptive analysis can lead to false discoveries, and proposing methods to mitigate this bias.

Contribution

It proposes a mutual information-based framework to measure and bound exploration bias, connecting it to privacy concepts and offering randomized techniques for bias reduction.

Findings

Mutual information bounds are tight in natural settings.

Analysis of bias in filtering, rank selection, and clustering.

Randomization techniques can reduce exploration bias effectively.

Abstract

Modern data is messy and high-dimensional, and it is often not clear a priori what are the right questions to ask. Instead, the analyst typically needs to use the data to search for interesting analyses to perform and hypotheses to test. This is an adaptive process, where the choice of analysis to be performed next depends on the results of the previous analyses on the same data. Ultimately, which results are reported can be heavily influenced by the data. It is widely recognized that this process, even if well-intentioned, can lead to biases and false discoveries, contributing to the crisis of reproducibility in science. But while %the adaptive nature of exploration any data-exploration renders standard statistical theory invalid, experience suggests that different types of exploratory analysis can lead to disparate levels of bias, and the degree of bias also depends on the particulars of the data set. In this paper, we propose a general information usage framework to quantify and provably bound the bias and other error metrics of an arbitrary exploratory analysis. We prove that our mutual information based bound is tight in natural settings, and then use it to give rigorous insights into when commonly used procedures do or do not lead to substantially biased estimation. Through the lens of information usage, we analyze the bias of specific exploration procedures such as filtering, rank selection and clustering. Our general framework also naturally motivates randomization techniques that provably reduces exploration bias while preserving the utility of the data analysis. We discuss the connections between our approach and related ideas from differential privacy and blinded data analysis, and supplement our results with illustrative simulations.