High Quality Content by WIKIPEDIA articles! In statistics and machine learning, Rademacher complexity, named after Hans Rademacher, measures richness of a class of real-valued functions with respect to a probability distribution. Let mathcal{F} be a class of real-valued functions defined on a domain space Z. The empirical Rademacher complexity of mathcal{F} on a sample S=(z_1, z_2, dots, z_m) in Z^m is defined as widehat mathcal{R}_S(mathcal{F}) = frac{2}{m} sup_{f in mathcal{F}} left| sum_{i=1}^m sigma_i f(z_i) right| where sigma_1, sigma_2, dots, sigma_m are independent random variables such that Pr(sigma_i = +1) = Pr(sigma_i = -1) = 1/2 for any i=1,2,dots,m. The random variables sigma_1, sigma_2, dots, sigma_m are referred to as Rademacher variables.

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