Efficient Adaptive Data Analysis over Dense Distributions

Modern data workflows are inherently adaptive, repeatedly querying the same dataset to refine and validate sequential decisions, but such adaptivity can lead to overfitting and invalid statistical inference. Adaptive Data Analysis (ADA) mechanisms address this challenge; however, there is a fundamental tension between computational efficiency and sample complexity. For $T$ rounds of adaptive analysis, computationally efficient algorithms typically incur suboptimal $O(\sqrt{T})$ sample complexity, whereas statistically optimal $O(\log T)$ algorithms are computationally intractable under standard cryptographic assumptions. In this work, we shed light on this trade-off by identifying a natural class of data distributions under which both computational efficiency and optimal sample complexity are achievable. We propose a computationally efficient ADA mechanism that attains optimal $O(\log T)$ sample complexity when the data distribution is dense with respect to a known prior. This setting includes, in particular, feature–label data distributions arising in distribution-specific learning. As a consequence, our mechanism also yields a sample-efficient (i.e., $O(\log T)$ samples) statistical query oracle in the distribution-specific setting. Moreover, although our algorithm is not based on differential privacy, it satisfies a relaxed privacy notion known as Predicate Singling Out (PSO) security (Cohen and Nissim, 2020). Our results thus reveal an inherent connection between adaptive data analysis and privacy beyond differential privacy.

💡 Research Summary

The paper tackles a central open problem in adaptive data analysis (ADA): achieving the statistically optimal O(log T) sample complexity for T rounds of adaptively chosen queries while maintaining computational efficiency. Prior work shows a stark trade‑off: algorithms that run in polynomial time typically need Ω(√T) samples, and the O(log T) sample bound is only attainable by computationally intractable methods such as Private Multiplicative Weights (PMW). The authors observe that existing hardness results assume the mechanism must work for any data distribution, prompting the question of whether a natural subclass of distributions permits both efficiency and optimal sample usage.

They define a class of dense distributions with respect to a known prior distribution D_g generated by an efficiently computable function g. A target distribution D is λ‑dense if for every element i, Pr_D