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作者：Ren, Zhao; Zhou, Harrison H.
作者单位：Yale University
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作者：Zhao, Yunpeng; Levina, Elizaveta; Zhu, Ji
作者单位：George Mason University; University of Michigan System; University of Michigan
摘要：Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of community detection under the block model have been recently developed. However, the block model is limited by its assumption that all nodes within a community are stochastically equivalent, and provides a poor fit to networks with hubs or highly varying node d...
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作者：Lee, Young K.; Mammen, Enno; Park, Byeong U.
作者单位：Kangwon National University; University of Mannheim; Seoul National University (SNU)
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作者：Cai, Tony; Yuan, Ming
作者单位：University of Pennsylvania; University System of Georgia; Georgia Institute of Technology
摘要：Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by care...
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作者：Yuan, Ming
作者单位：University System of Georgia; Georgia Institute of Technology
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作者：Candes, Emmanuel J.; Soltanolkotabi, Mahdi
作者单位：Stanford University
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作者：Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S.
作者单位：California Institute of Technology; Massachusetts Institute of Technology (MIT)
摘要：Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of latent components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in which the latent and observed variables are jointly Gaussian, with the conditional statistics of the o...
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作者：Castillo, Ismael; van der Vaart, Aad
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Vrije Universiteit Amsterdam
摘要：We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero means and next a prior on the nonzero values. We consider the posterior distribution in the frequentist set-up that the observations are generated according to a fixed mean vector, and are interested in the posterior distribution of the number of nonzero co...
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作者：Chandrasekaran, Venkat; Parrilo, Pablo A.; Willsky, Alan S.
作者单位：California Institute of Technology; Massachusetts Institute of Technology (MIT)
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作者：Giraud, Christophe; Tsybakov, Alexandre
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; ENSAE Paris
