Uniform estimation of nonlinear statistics
Andreas Maurer -
For nearly two decades the method of Rademacher and Gaussian complexities has been used to prove generalization bounds in learning theory, typically by showing that the sample mean is a good estimate of the mean uniformly over some loss-class, if the complexity of the loss class is not too big. Many powerful tricks to bound Rademacher or Gaussian complexities have been developed along this line of work. My talk is about an extension of this method to cases where the sample mean is replaced by a nonlinear statistic satisfying certain first- and second-order Lipschitz conditions. I will explain these conditions, sketch a proof and discuss some applications, such as the generalization of recently proposed algorithms optimizing the partial AUC.
Andreas worked in machine vision, image processing and machine learning since 1983. He is an active and independent researcher in probability theory, machine learning and statistics.
2019-12-03 at 3:00 pm (subject to variability)