# Testing Properties of Multiple Distributions with Few Samples

arXiv: https://arxiv.org/abs/1911.07324 · HTML: https://mlsanity.com/paper/1911.07324/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [Optimal Algorithms for Augmented Testing of Discrete Distributions](https://mlsanity.com/paper/2412.00974/) (2024)
- [Testing with Non-identically Distributed Samples](https://mlsanity.com/paper/2311.11194/) (2023)
- [Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions](https://mlsanity.com/paper/2603.04635/) (2026)

## Abstract (arXiv)

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from s distributions, p1, p2, ldots, ps, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the pi's are uniform or ε-far from being uniform in ℓ1-distance (2) Identity Testing: Testing whether all the pi's are equal to an explicitly given distribution q or ε-far from q in ℓ1-distance, and (3) Closeness Testing: Testing whether all the pi's are equal to a distribution q which we have sample access to, or ε-far from q in ℓ1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.