Information, Privacy and Stability in Adaptive Data Analysis
This is an incremental review that synthesizes known results on adaptive data analysis, focusing on information-theoretic concepts for researchers in statistics and machine learning.
The paper addresses the challenge of drawing statistically valid conclusions when data are re-used across adaptive analyses, where later stages depend on earlier results, and highlights that limiting information revealed in earlier stages controls bias in later stages.
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be performed at a given stage depends on the results of earlier stages. Such dependency can arise when the same data are used by several scientific studies, or when a single analysis consists of multiple stages. How can we draw statistically valid conclusions when data are re-used? This is the focus of a recent and active line of work. At a high level, these results show that limiting the information revealed by earlier stages of analysis controls the bias introduced in later stages by adaptivity. Here we review some known results in this area and highlight the role of information-theoretic concepts, notably several one-shot notions of mutual information.