Almost Optimal Distribution-free Junta Testing

01/01/2019

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by   Nader H. Bshouty, et al.

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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 Õ(k^2)/ϵ queries. In this paper, we give a simple two-sided error adaptive algorithm that makes Õ(k/ϵ) queries.