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作者：Belitser, Eduard; Ghosal, Subhashis
作者单位：Vrije Universiteit Amsterdam; North Carolina State University
摘要：We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an excessive bias restriction condition. This condition gives rise to a new slicing of the entire space that is suitable for ensuring unifo...
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作者：Javanmard, Adel; Mondelli, Marco; Montanari, Andrea
作者单位：University of Southern California; Institute of Science & Technology - Austria; Stanford University; Stanford University
摘要：Fitting a function by using linear combinations of a large number N of simple components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is nonconvex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here, we consider the proble...
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作者：Drton, Mathias; Han, Fang; Shi, Hongjian
作者单位：Technical University of Munich; University of Washington; University of Washington Seattle
摘要：Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting nonlinear, nonmonotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence. Built upon a newly de...
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作者：Mao, Cheng; Pananjady, Ashwin; Wainwright, Martin J.
作者单位：University System of Georgia; Georgia Institute of Technology; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Many applications, including rank aggregation, crowd-labeling and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a subset of) its entries. We design and analyze polynomial-time algorithms that improve upon the state of the art in two distinct metrics, showing, in particular, that minimax optimal...
