Preserving Statistical Validity in Adaptive Data Analysis

Abstract: A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of $m$ adaptively chosen functions on an unknown distribution given $n$ random samples. We show that, surprisingly, there is a way to estimate an exponential in $n$ number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

• The paper introduces a differential privacy framework that preserves the accuracy of adaptively chosen statistical queries.
• It demonstrates that an exponential number of adaptive queries can be estimated accurately using novel privacy-preserving algorithms.
• The work bridges theoretical inference and practical data analysis, ensuring robust generalization from reused datasets.

Overview of "Preserving Statistical Validity in Adaptive Data Analysis"

The paper "Preserving Statistical Validity in Adaptive Data Analysis" by Cynthia Dwork et al. examines a pressing issue in current statistical data analysis: the reliability of statistical inference when hypotheses and analyses are adaptively chosen based on the same dataset. The authors identify a fundamental discrepancy between theoretical statistical inference and practical data analysis, where data is reused and hypotheses evolve based on exploratory data analysis.

Main Contributions

The primary contribution of this work is a novel approach that ensures the statistical validity of results in adaptive data analysis settings. Unlike traditional approaches, which often demand fresh data for each analysis to prevent overfitting and overclaiming of statistical significance, the authors leverage techniques from differential privacy to mitigate the pitfalls of adaptive analyses.

1. Adaptive Statistical Queries: The paper tackles the challenge of estimating the expectations of adaptively chosen functions on an unknown distribution based on a single dataset. The authors show that, counterintuitively, it is possible to estimate an exponential number of such expectations accurately, surpassing the capabilities of standard empirical estimators that handle only a linear number of estimates.
2. Techniques from Differential Privacy: Central to this breakthrough is the use of techniques developed for differential privacy. These techniques control the interaction between the data analyst and the dataset, ensuring that the sequence of chosen functions does not lead to overfitting. Specifically, the authors demonstrate that by actively perturbing estimates and coordinating these estimates through privacy-preserving mechanisms, one can enhance the accuracy and validity of results.
3. Theoretical and Practical Implications: The paper provides both theoretical insights and practical algorithms. It delivers a transfer theorem that any analysis performed via a differentially private algorithm generalizes well to the underlying distribution. This result implies that differential privacy not only protects individual data privacy but also ensures the validity of data analysis in adaptive settings.

Detailed Results

• Exponential Improvement: The paper establishes that it is possible to answer an exponential number of adaptively chosen statistical queries with high accuracy. This finding signifies a significant improvement over traditional empirical approaches and highlights the value of privacy-preserving techniques in data analysis beyond privacy concerns.
• Efficient Algorithms: Despite the inherent complexity of the task, the authors present efficient algorithms underpinned by differential privacy principles. These algorithms demonstrate the practical feasibility of their methods for use in real-world adaptive data analysis scenarios.
• Generalization of Queries: By proving a connection between differential privacy and generalization, the authors offer a novel perspective on how queries that are generated by differentially private algorithms can be as robust as those generated non-adaptively.

Implications and Future Directions

The findings of this paper have substantial implications for both data science practice and theory. The ability to preserve statistical validity without requiring fresh data opens new avenues for efficiently utilizing existing datasets in ongoing analyses. Moreover, the connection drawn between differential privacy and statistical validity suggests broader applications in fields reliant on adaptive data analysis, such as machine learning and AI.

For future research, one promising direction is the exploration of other privacy-preserving frameworks that could further enhance the capabilities of adaptive data analysis. Additionally, applying these insights to complex multivariate testing problems or cross-domain analyses could yield significant advancements in scientific methodologies.

In conclusion, this work marks an important step in aligning theoretical principles of statistical inference with the practical realities of data analysis in the era of big data and open science. By leveraging concepts from differential privacy, the authors provide a robust framework for maintaining the integrity and reliability of statistical conclusions drawn from adaptively reused datasets.