DICTATOR FUNCTIONS MAXIMIZE MUTUAL INFORMATION

• 成果类型: Article
• 署名作者: Pichler, Georg; Piantanida, Pablo; Matz, Gerald
• 署名单位: Technische Universitat Wien; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1384
• 发表日期: 2018
• 页码: 3094-3101
• 关键词: boolean functions

摘要

Let (X, Y) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X, Y). We prove that the inequality I( f (X); g (Y)) <= I(X; Y) holds for any two Boolean functions: f, g: {-1,1}(n) -> {-1,1} [I(.;.) denotes mutual information]. We further show that equality in general is achieved only by the dictator functions f(x) = +/- g(x) = +/- x(i), i is an element of {1,2,...,n}.