Optimal Support Size Testing

Qisheng Wang

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arXiv · 2610.18723

Optimal Support Size Testing

Qisheng Wang

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Abstract

We present an optimal tester for support size that determines whether an unknown probability distribution is supported on $n$ elements or $\varepsilon$-far away (in total variation distance) with sample complexity $Θ(\frac{n}{\varepsilon\log(n)})$, improving the prior best $O(\frac{n}{\varepsilon\log(n)} \log(\min\{\frac{1}{\varepsilon}, n\}))$ due to Ferreira Pinto Jr. and Harms (STOC 2025). As a generalization, we provide a pretty good lower bound on support size.

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Qisheng Wang. 2026-10-13. Optimal Support Size Testing. https://arxiv.org/abs/2610.18723

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