Almost Optimal Distribution-free Junta Testing
(1901.00717)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 $\tilde O(k2)/\epsilon$ queries. In this paper, we give a simple two-sided error adaptive algorithm that makes $\tilde O(k/\epsilon)$ queries.
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