@inproceedings{8a39f9cff92d4c4094068c8bc59e1e8e,
title = "Almost Optimal Proper Learning and Testing Polynomials",
abstract = "We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For s-sparse polynomial over n variables and ϵ= 1 / sβ, β> 1, our algorithm makes (formula presetend) qU=(sϵ)logββ+O(1β)+O~(s)(log1ϵ)logn queries. Notice that our query complexity is sublinear in 1 / ϵ and almost linear in s. All previous algorithms have query complexity at least quadratic in s and linear in 1 / ϵ. We then prove the almost tight lower bound (formula presented) qL=(sϵ)logββ+Ω(1β)+Ω(s)(log1ϵ)logn, Applying the reduction in [9] with the above algorithm, we give the first almost optimal polynomial-time tester for s-sparse polynomial. Our tester, for β> 3.404, makes(formula presentes)O~(sϵ) queries.",
keywords = "Polynomial, Proper learning, Property testing",
author = "Bshouty, {Nader H.}",
note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.; 15th Latin American Symposium on Theoretical Informatics, LATIN 2022 ; Conference date: 07-11-2022 Through 11-11-2022",
year = "2022",
doi = "https://doi.org/10.1007/978-3-031-20624-5_19",
language = "الإنجليزيّة",
isbn = "9783031206238",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "312--327",
editor = "Armando Casta{\~n}eda and Francisco Rodr{\'i}guez-Henr{\'i}quez",
booktitle = "LATIN 2022",
address = "ألمانيا",
}