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作者：Padoan, Simone A.; Rizzelli, Stefano
作者单位：Bocconi University; Catholic University of the Sacred Heart
摘要：Predicting extreme events is important in many applications in risk analysis. Extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. In this paper we focus on a semiparametric B...
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作者：Liang, Tengyuan; Sur, Pragya
作者单位：University of Chicago; Harvard University
摘要：This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) p scales with the sample size n, in an overparametrized regime. Under a class of statistical models, we provide an exact analysis of the generalization error of boosting when the algorithm interpolates the training data and maximizes the empirical l(1)-margin. Fu...
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作者：Berthet, Philippe; Einmahl, John H. J.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Tilburg University
摘要：Given n independent random vectors with common density f on R-d, we study the weak convergence of three empirical-measure based estimators of the convex lambda-level set L-lambda of f, namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains L-lambda. Since these set-valued estimators approach L-lambda, even the formulation of their weak convergence is nonstandard. We identify the joint limiting distribution of...
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作者：Niles-Weed, Jonathan; Berthet, Quentin
作者单位：New York University; Alphabet Inc.; Google Incorporated
摘要：We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates for this problem for general Wasserstein distances for two classes of densities: smooth probability densities on [0, 1](d) bounded away from 0, and sub-Gaussian densities lying in the Holder class C-s, s is an element of (0, 1). Unlike classical nonparametri...
