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 functions is measured with respect to an arbitrary and unknown probability distribution over {0,1}^n. Chen, Liu, Servedio, Sheng and Xie [Zhengyang Liu et al., 2018] showed that the distribution-free k-junta testing can be performed, with one-sided error, by an adaptive algorithm that makes O~(k^2)/epsilon queries. In this paper, we give a simple two-sided error adaptive algorithm that makes O~(k/epsilon) queries.
@InProceedings{bshouty:LIPIcs.CCC.2019.2, author = {Bshouty, Nader H.}, title = {{Almost Optimal Distribution-Free Junta Testing}}, booktitle = {34th Computational Complexity Conference (CCC 2019)}, pages = {2:1--2:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-116-0}, ISSN = {1868-8969}, year = {2019}, volume = {137}, editor = {Shpilka, Amir}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.2}, URN = {urn:nbn:de:0030-drops-108249}, doi = {10.4230/LIPIcs.CCC.2019.2}, annote = {Keywords: Distribution-free property testing, k-Junta} }
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