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作者：Manole, Tudor; Balakrishnan, Sivaraman; Niles-Weed, Jonathan; Wasserman, Larry
作者单位：Carnegie Mellon University; New York University; New York University
摘要：We analyze a number of natural estimators for the optimal transport map between two distributions and show that they are minimax optimal. We adopt the plugin approach: our estimators are simply optimal couplings between measures derived from our observations, appropriately extended so that they define functions on Rd. d . When the underlying map is assumed to be Lipschitz, we show that computing the optimal coupling between the empirical measures, and extending it using linear smoothers, alrea...
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作者：Song, Yanglei; Fellouris, Georgios
作者单位：Queens University - Canada; University of Illinois System; University of Illinois Urbana-Champaign
摘要：A novel sequential change detection problem is proposed, in which the goal is to not only detect but also accelerate the change. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time. The assigned treatments determine the pre-change and post-change distributions of the responses and also influence when the change happens. The goal is to find a treatment assignment rule and a stopping rule that minimize the expected total numb...
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作者：Zrnic, Tijana; Fithian, William
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, , which delivers valid answers to the set of all questions that could possibly have been asked. However, simultaneous inference can be unnecessarily conservative if this set includes many questions that were unlikely to be asked in the first place. We introduce a less conservative solution to selective inferenc...
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作者：Bastian, Patrick; Dette, Holger; Heiny, Johannes
作者单位：Ruhr University Bochum; Stockholm University
摘要：This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g., all pairwise Kendall's tau) between the components vanish, we are interested in the (null) hypothesis that all pairwise associations do not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in the high-dimensional regime, it is rare, and pe...
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作者：Laha, Nilanjana; Sonabend-w, Aaron; Mukherjee, Rajarshi; Cai, Tianxi
作者单位：Texas A&M University System; Texas A&M University College Station; Harvard University
摘要：Large health care data repositories such as electronic health records (EHR) open new opportunities to derive individualized treatment strategies for complicated diseases such as sepsis. In this paper, we consider the problem of estimating sequential treatment rules tailored to a patient's individual characteristics, often referred to as dynamic treatment regimes (DTRs). Our main objective is to find the optimal DTR that maximizes a discontinuous value function through direct maximization of Fi...
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作者：Ohn, Ilsang; Lin, Lizhen
作者单位：Inha University; University System of Maryland; University of Maryland College Park
摘要：In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally tractable variational Bayes method that performs adaptive inference. To fill this gap, we propose a novel adaptive variational Bayes framework, which can operate on a collection of models. The proposed framework first computes a variational posterior over each...
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作者：Yang, Songshan; Zheng, Shurong; Li, Runze
作者单位：Renmin University of China; Renmin University of China; Northeast Normal University - China; Northeast Normal University - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with high-dimensional two-sample mean problems, which receive considerable attention in recent literature. To utilize the correlation information among variables for enhancing the power of two- sample mean tests, we consider the setting in which the precision matrix of high-dimensional data possesses a linear structure. Thus, we first propose a new precision matrix estimation procedure with considering its linear structure, and further develop regularization methods to ...
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作者：Xu, Haotian; Wang, Daren; Zhao, Zifeng; Yu, Yi
作者单位：University of Warwick; University of Notre Dame; University of Notre Dame
摘要：This paper concerns the limiting distributions of change-point estimators, in a high-dimensional linear regression time-series context, where a regression object (y(t), X-t) is an element of R x R-p is observed at every time point t is an element of{1 , ... , n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in l(2)-norm. We provide limiting distributions of the change-point estimators in the regimes where the minimal jump size v...
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作者：Bhattacharya, Sohom; Fan, Jianqing; Mukherjee, Debarghya
作者单位：State University System of Florida; University of Florida; Princeton University; Boston University
摘要：Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed, and consequently, they ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper, we bridge t...
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作者：Durante, Daniele; Pozza, Francesco; Szabo, Botond
作者单位：Bocconi University; Bocconi University
摘要：Gaussian deterministic approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. While these approximations are justified, in asymptotic regimes, by Bernstein-von Mises type results, in practice the expected Gaussian behavior might poorly represent the actual shape of the target posterior, thus affecting approximation accuracy. Motivated by these considerations, we derive an improved class of closed-form and valid deterministic app...
