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- W1894098103 abstract "There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size $k$. We study two of the most important tests under the conditional-sampling model where each query specifies a subset $S$ of the domain, and the response is a sample drawn from $S$ according to the underlying distribution. For identity testing, which asks whether the underlying distribution equals a specific given distribution or $epsilon$-differs from it, we reduce the known time and sample complexities from $tilde{mathcal{O}}(epsilon^{-4})$ to $tilde{mathcal{O}}(epsilon^{-2})$, thereby matching the information theoretic lower bound. For closeness testing, which asks whether two distributions underlying observed data sets are equal or different, we reduce existing complexity from $tilde{mathcal{O}}(epsilon^{-4} log^5 k)$ to an even sub-logarithmic $tilde{mathcal{O}}(epsilon^{-5} log log k)$ thus providing a better bound to an open problem in Bertinoro Workshop on Sublinear Algorithms [Fisher, 2004]." @default.
- W1894098103 created "2016-06-24" @default.
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- W1894098103 date "2015-04-16" @default.
- W1894098103 modified "2023-09-27" @default.
- W1894098103 title "Faster Algorithms for Testing under Conditional Sampling" @default.
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- W1894098103 hasPublicationYear "2015" @default.
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