Optimal Rates for Differentially Private Hypothesis Testing with E-values
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910278456705024 |
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| author | Jacobsen, Ben Gonzalez, Tomas Brown, Gavin Fawaz, Kassem Ramdas, Aaditya |
| author_facet | Jacobsen, Ben Gonzalez, Tomas Brown, Gavin Fawaz, Kassem Ramdas, Aaditya |
| contents | E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Rates for Differentially Private Hypothesis Testing with E-values Jacobsen, Ben Gonzalez, Tomas Brown, Gavin Fawaz, Kassem Ramdas, Aaditya Cryptography and Security Data Structures and Algorithms Information Theory Machine Learning Statistics Theory E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels. |
| title | Optimal Rates for Differentially Private Hypothesis Testing with E-values |
| topic | Cryptography and Security Data Structures and Algorithms Information Theory Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2605.28952 |