Almost Optimal Distribution-free Junta Testing

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.

arXiv commentarXiv admin note: text overlap with arXiv:1802.04859 by other authors