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作者：Kur, Gil; Gao, Fuchang; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Idaho; University of California System; University of California Berkeley; Columbia University
摘要：Under the usual nonparametric regression model with Gaussian errors, are shown to be suboptimal for estimating a d-dimensional convex function in squared error loss when the dimension d is 5 or larger. The specific function classes considered include: (i) bounded convex functions supported on a polytope (in random design), (ii) Lipschitz convex functions supported on any convex domain (in random design) and (iii) convex functions supported on a polytope (in fixed design). For each of these cla...
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作者：Qiu, Hongxiang; Tchetgen, Eric Tchetgen; Dobriban, Edgar
作者单位：Michigan State University; University of Pennsylvania
摘要：Statistical machine learning methods often face the challenge of limited data available from the population of interest. One remedy is to leverage data from auxiliary source populations, which share some conditional distributions or are linked in other ways with the target domain. Techniques leveraging such dataset shift conditions are known as domain adaptation or transfer learning. . Despite extensive literature on dataset shift, limited works address how to efficiently use the auxiliary pop...
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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. ...
