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作者：Li, Gen; Shi, Laixi; Chen, Yuxin; Chi, Yuejie; Wei, Yuting
作者单位：Chinese University of Hong Kong; California Institute of Technology; University of Pennsylvania; Carnegie Mellon University
摘要：This paper is concerned with offline reinforcement learning (RL), which learns using precollected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior results either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality, thus posing an impediment to efficient offline RL in sample-starved applications. We demonstrate that the model-based (or plug-in) approach ac...
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作者：Wang, Wen; Wu, Shihao; Zhu, Ziwei; Zhou, Ling; Song, Peter X. -K.
作者单位：University of Michigan System; University of Michigan; University of Michigan System; University of Michigan; Southwestern University of Finance & Economics - China
摘要：Fusing regression coefficients into homogeneous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called L-0-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called MSE grouping sensitivity that underp...
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作者：Brutsche, Johannes; Rohde, Angelika
作者单位：University of Freiburg
摘要：Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift b to some reference drift b0: At prescribed significance, we simultaneously identify those regions where violation from similarity occurs, without a priori knowledge of their number, size and location. This test is shown to be minimax-optimal and adaptive. At the same time, the procedure is robust under small deviation from Brownian motion as the driving noise process. A detailed ...
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作者：Zhou, Yeqing; Xu, Kai; Zhu, Liping; Li, Runze
作者单位：Tongji University; Tongji University; Anhui Normal University; Renmin University of China; Zhejiang Gongshang University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's D, Blum-Kiefer-Rosenblatt's R and Bergsma-Dassios-Yanagimoto's tau(& lowast;). Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transform...
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作者：Rajaraman, Nived; Han, Yanjun; Jiao, Jiantao; Ramchandran, Kannan
作者单位：University of California System; University of California Berkeley; New York University; New York University
摘要：We consider the sequential decision-making problem where the mean outcome is a nonlinear function of the chosen action. Compared with the linear model, two curious phenomena arise in nonlinear models: first, in addition to the learning phase with a standard parametric rate for estimation or regret, there is an burn-in period with a fixed cost determined by the nonlinear function; second, achieving the smallest burn-in cost requires new exploration algorithms. For a special family of nonlinear ...
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作者：Cattaneo, Matias D.; Jansson, Michael; Nagasawa, Kenichi
作者单位：Princeton University; University of California System; University of California Berkeley; University of Warwick
摘要：Westling and Carone ( Ann. Statist. 48 (2020) 1001-1024) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution of those estimators is representable as the left derivative of the greatest convex minorant of a Gaussian process whose monomial mean can be of unknown order (when the degree of flatness of the function of interest is unknown)....
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作者：Li, Degui; Li, Runze; Shang, Han Lin
作者单位：University of Macau; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Macquarie University
摘要：We consider detecting and estimating breaks in heterogenous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where the proposed test ...
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作者：Rousseau, Judith; Scricciolo, Catia
作者单位：University of Oxford; University of Verona
摘要：We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors with independent coordinates having ordinary smooth densities, we derive an inversion inequality relating the L-1-Wasserstein distance between two distributions of the signal to the L-1-distance between the corresponding mixture densities of the observations. ...
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作者：Buecher, Axel; Pakzad, Cambyse
作者单位：Ruhr University Bochum; Inria; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA)
摘要：Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature by considering tests that allow to detect higher-order dependencies. The proposed methods are based on connecting the problem to copulas and making use of the Moebius transformation of the empirical copula process; an approach that is related to Lancaster int...
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作者：Nickl, Richard; Titi, Edriss s.
作者单位：University of Cambridge; University of Cambridge
摘要：We consider a nonlinear Bayesian data assimilation model for the periodic two-dimensional Navier-Stokes equations with initial condition modelled by a Gaussian process prior. We show that if the system is updated with sufficiently many discrete noisy measurements of the velocity field, then the posterior distribution eventually concentrates near the ground truth solution of the time evolution equation, and in particular that the initial condition is recovered consistently by the posterior mean...
