# Fourier-Based Testing for Families of Distributions

@article{Canonne2017FourierBasedTF, title={Fourier-Based Testing for Families of Distributions}, author={Cl{\'e}ment L. Canonne and Ilias Diakonikolas and Alistair Stewart}, journal={Electron. Colloquium Comput. Complex.}, year={2017}, volume={TR17} }

We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution $\mathbf{P}$, we want to distinguish (with high probability) between the case that $\mathbf{P} \in \mathcal{P}$ and the case that $\mathbf{P}$ is $\epsilon$-far, in total variation distance, from every distribution in $\mathcal{P}$. This is the prototypical…

## 8 Citations

### Testing for Families of Distributions via the Fourier Transform

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This work applies its Fourier-based framework to obtain near sample-optimal and computationally efficient testers for the following fundamental distribution families: Sums of Independent Integer Random Variables, Poisson Multinomial Distributions, and Discrete Log-Concave Distributions.

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The new upper and lower bounds show that the optimal sample complexity of identity testing is $\Theta\left( \frac{1}{\epsilon^2}\left(\sqrt{n \log(1/\delta)} + \log (1/ \delta) \right)\right) for any $n, \ep silon$, and $\delta$.

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### Private Testing of Distributions via Sample Permutations

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The framework of property testing is used to design algorithms to test the properties of the distribution that the data is drawn from with respect to differential privacy, which indicates that differential privacy can be obtained in most regimes of parameters for free.

### Modern challenges in distribution testing

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The goal of this dissertation is to identify and address several contemporary challenges in distribution testing and make progress in answering the following questions.

### Property Testing and Probability Distributions: New Techniques, New Models, and New Goals

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Property Testing and Probability Distributions: New Techniques, New Models, and New Goals Clément L. Canonne Recently there has been a lot of glorious hullabaloo about Big Data and how it is going to…

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