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arXiv · 1901.00717

Almost Optimal Distribution-free Junta Testing

Nader H. Bshouty
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Abstract

We consider the problem of testing whether an unknown $n$-variable Boolean function is a $k$-junta in the distribution-free property testing model, where the distance between function is measured with respect to an arbitrary and unknown probability distribution over $\{0,1\}^n$. Chen, Liu, Servedio, Sheng and Xie showed that the distribution-free $k$-junta testing can be performed, with one-sided error, by an adaptive algorithm that makes $\tilde O(k^2)/\epsilon$ queries. In this paper, we give a simple two-sided error adaptive algorithm that makes $\tilde O(k/\epsilon)$ queries.

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Nader H. Bshouty. 2019-01-01. Almost Optimal Distribution-free Junta Testing. https://arxiv.org/abs/1901.00717

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