Asymptotic sequential Rademacher complexity of a finite function class

Abstract

Abstract. For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a G-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional G-normal random variable. We illustrate this result by deriving upper and lower bounds for the asymptotic sequential Rademacher complexity.

Optimal unbiased estimation for maximal distribution

“…The above statistic is not an efficient way to use samples. We refer to [14,15], for how to efficiently use the real world data to estimate the upper and lower volatilities of daily return. Extensive experiments on both NASDAQ Composite Index and S&P500 Index demonstrate the excellent performence of G-VaR, a new benchmark predictor for value-at-risk based on this new maximal estimator, which is superior to most existing benchmark VaR predictors.…”

Pde Approach to the Problem of Online Prediction With Expert Advice: A Construction of Potential-Based Strategies

“…The described approach is mainly inspired by the paper [6], where there was studied a link between fully non-linear second order (parabolic and elliptic) PDE and repeated games. Its application to the problems of online learning theory was initiated in [10], where an asymptotics of the sequential Rademacher complexity (the last notion was introduced in [8]) of a finite function class was related to the viscosity solution of a G-heat equation. In turn, the result of [10] is based on the central limit theorem under model uncertainty, studied within the same approach in [9].…”