Learning low-degree functions on the discrete hypercube

题目：Learning low-degree functions on the discrete hypercube

报告人：Alexandros Eskenazis（Centre national de la recherche scientifique, CNRS）

时间：2022年12月7日（星期三），16:00-17:30

Zoom会议：会议号：882 8540 7533，会议密码：028422

会议链接：https://zoom.us/j/88285407533?pwd=NFlsWlZlb2F3c3VmMHBqOXVud1NpQT09

摘要：Let f be an unknown function on the n-dimensional discrete hypercube. How many values of f do we need in order to approximately reconstruct the function? In this talk, we shall discuss the random query model for this fundamental problem from computational learning theory. We will explain a newly discovered connection with a family of polynomial inequalities going back to Littlewood (1930) which will in turn allow us to derive sharper estimates for the query complexity of this model, exponentially improving those which follow from the classical Low-Degree Algorithm of Linial, Mansour and Nisan (1989), while maintaining a running time of the same order. Time permitting, we will also show a matching information-theoretic lower bound. Based on joint works with Paata Ivanisvili (UC Irvine) and Lauritz Streck (Cambridge).

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