Locally Private Non-Asymptotic Testing of Discrete Distributions Is Faster Using Interactive Mechanisms

Abstract

We find separation rates for testing multinomial or more general discrete distributions under the constraint of alpha-local differential privacy. We construct efficient randomized algorithms and test procedures, in both the case where only non-interactive privacy mechanisms are allowed and also in the case where all sequentially interactive privacy mechanisms are allowed. The separation rates are faster in the latter case. We prove general information theoretical bounds that allow us to establish the optimality of our algorithms among all pairs of privacy mechanisms and test procedures, in most usual cases. Considered examples include testing uniform, polynomially and exponentially decreasing distributions.

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Text

Berrett and Butucea. "Locally Private Non-Asymptotic Testing of Discrete Distributions Is Faster Using Interactive Mechanisms." Neural Information Processing Systems, 2020.

Markdown

[Berrett and Butucea. "Locally Private Non-Asymptotic Testing of Discrete Distributions Is Faster Using Interactive Mechanisms." Neural Information Processing Systems, 2020.](https://mlanthology.org/neurips/2020/berrett2020neurips-locally/)

BibTeX

@inproceedings{berrett2020neurips-locally,
  title     = {{Locally Private Non-Asymptotic Testing of Discrete Distributions Is Faster Using Interactive Mechanisms}},
  author    = {Berrett, Thomas and Butucea, Cristina},
  booktitle = {Neural Information Processing Systems},
  year      = {2020},
  url       = {https://mlanthology.org/neurips/2020/berrett2020neurips-locally/}
}