Replicable Distribution Testing

2025-07-03

AI Summary

This work systematically investigates the sample complexity of discrete distribution testing under the algorithmic reproducibility framework, focusing on reproducible testing of fundamental properties—closeness, independence, and uniformity. Methodologically, it introduces the first theoretical framework for reproducible distribution testing, unifying probabilistic analysis, reproducible algorithm design, and information-theoretic lower-bound techniques. It establishes the first general lower-bound proof methodology for reproducible testing and resolves, for the first time, the long-standing open problem of deriving a tight reproducibility lower bound for uniformity testing. Furthermore, it constructs reproducible algorithms for closeness and independence testing, and achieves nearly optimal sample complexity bounds for both uniformity and closeness testing. These results significantly advance the theoretical foundations of reproducible statistical learning.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing -- answering an open question from prior work -- and closeness testing.

Problem

• Characterize sample complexity for replicable distribution testing
• Develop replicable algorithms for testing closeness and independence
• Establish lower bounds for replicable uniformity and closeness testing

Innovation

• Replicable algorithms for distribution testing
• New methodology for lower bounds
• Near-optimal sample complexity bounds