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作者：Jiang, Sheng; Tokdar, Surya T.
作者单位：Duke University
摘要：Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable selection, are known to also adapt to the unknown intrinsic dimension of a sparse true regression function. But it remains unclear if such extensions offer variable selection consistency, that is, if the true subset of important variables could be consistently l...
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作者：Cai, T. Tony; Wang, Yichen; Zhang, Linjun
作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
摘要：Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the (s, 8)-differential privacy...
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作者：Han, Qiyang
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper bound for the convergence rates thus obtained typically matches the minimax lower bound when the entropy integral converges, but admits a strict gap compared to the lower bound when it diverges. Birge and Massart (Probab. Theory Related Fields 97 (1993) 113...
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作者：Ortelli, Francesco; van de Geer, Sara
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of (k - 1)th order differences. Our approach is based on combining a general oracle inequality for the l(1)-penalized least squares estimator with interpolating vectors to upper bound the effective sparsity. This allows one to show that the l(1)-penalty on the kth order differences leads to an estimator that can adapt to the number of jumps in the (k - 1)th order differences of the...
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作者：Wang, Chunyan; Mee, Robert W.
作者单位：Nankai University; Nankai University; University of Tennessee System; University of Tennessee Knoxville
摘要：Regular 2(n-P) designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to f-PFD with f > 3 is more challenging. This paper aims to study the general theory for the f-PFD for any f >= 3. We propose a method for obtaining the confounding frequency vectors for all nonequivalent f-PFDs, and to find the least G-aberration (or highest D-efficiency) f-PFD...
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作者：Lalancette, Michael; Engelke, Sebastian; Volgushev, Stanislav
作者单位：University of Toronto; University of Geneva
摘要：Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the latter setting is sca...
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作者：Catalano, Marta; Lijoi, Antonio; Prunster, Igor
作者单位：University of Warwick; Bocconi University
摘要：The proposal and study of dependent Bayesian nonparametric models has been one of the most active research lines in the last two decades, with random vectors of measures representing a natural and popular tool to define them. Nonetheless, a principled approach to understand and quantify the associated dependence structure is still missing. We devise a general, and not model-specific, framework to achieve this task for random measure based models, which consists in: (a) quantify dependence of a...
