
Statistical Inference in the Differential Privacy Model
In modern settings of data analysis, we may be running our algorithms on...
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Private TwoTerminal Hypothesis Testing
We study private twoterminal hypothesis testing with simple hypotheses ...
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A Rademacher Complexity Based Method fo rControlling Power and Confidence Level in Adaptive Statistical Analysis
While standard statistical inference techniques and machine learning gen...
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The Role of Interactivity in Local Differential Privacy
We study the power of interactivity in local differential privacy. First...
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Locally Private Hypothesis Testing
We initiate the study of differentially private hypothesis testing in th...
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Dataadaptive statistics for multiple hypothesis testing in highdimensional settings
Current statistical inference problems in areas like astronomy, genomics...
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Statistical Windows in Testing for the Initial Distribution of a Reversible Markov Chain
We study the problem of hypothesis testing between two discrete distribu...
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The Structure of Optimal Private Tests for Simple Hypotheses
Hypothesis testing plays a central role in statistical inference, and is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple hypotheses: given two distributions P and Q, and a privacy level ε, how many i.i.d. samples are needed to distinguish P from Q subject to εdifferential privacy, and what sort of tests have optimal sample complexity? Specifically, we characterize this sample complexity up to constant factors in terms of the structure of P and Q and the privacy level ε, and show that this sample complexity is achieved by a certain randomized and clamped variant of the loglikelihood ratio test. Our result is an analogue of the classical NeymanPearson lemma in the setting of private hypothesis testing. We also give an application of our result to the private changepoint detection. Our characterization applies more generally to hypothesis tests satisfying essentially any notion of algorithmic stability, which is known to imply strong generalization bounds in adaptive data analysis, and thus our results have applications even when privacy is not a primary concern.
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