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作者：Barber, Rina Foygel; Kolar, Mladen
作者单位：University of Chicago; University of Chicago
摘要：Understanding complex relationships between random variables is of fundamental importance in high-dimensional statistics, with numerous applications in biological and social sciences. Undirected graphical models are often used to represent dependencies between random variables, where an edge between two random variables is drawn if they are conditionally dependent given all the other measured variables. A large body of literature exists on methods that estimate the structure of an undirected g...
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作者：Lounici, Karim; Meziani, Katia; Peyre, Gabriel
作者单位：University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite PSL
摘要：In quantum optics, the quantum state of a light beam is represented through the Wigner function, a density on R-2, which may take negative values but must respect intrinsic positivity constraints imposed by quantum physics. In the framework of noisy quantum homodyne tomography with efficiency parameter 1/2 < eta <= 1, we study the theoretical performance of a kernel estimator of the Wigner function. We prove that it is minimax efficient, up to a logarithmic factor in the sample size, for the L...
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作者：Zhang, Xianyang; Yao, Shun; Shao, Xiaofeng
作者单位：Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang [J. Amer. Statist. Assoc. 109 (2014) 1302-1318], and it is able to detect certain type of departure from the null hypothesis of conditional mean independence without making any specific model assumptions. Theoretically, we estab...
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作者：Zheng, Qi; Peng, Limin; He, Xuming
作者单位：University of Louisville; Emory University; University of Michigan System; University of Michigan
摘要：Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equat...
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作者：Mousavi, Ali; Maleki, Arian; Baraniuk, Richard G.
作者单位：Rice University; Columbia University
摘要：This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as n, the number of observations, ...
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作者：Bi, Xuan; Qu, Annie; Shen, Xiaotong
作者单位：Yale University; Yunnan University; University of Illinois System; University of Illinois Urbana-Champaign; University of Minnesota System; University of Minnesota Twin Cities
摘要：Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this article, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested lat...
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作者：Gamarnik, David; Li, Quan
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We consider the problem of finding a k xk submatrix of an nxn matrix with i.i.d. standard Gaussian entries, which has a large average entry. It was shown in [Bhamidi, Dey and Nobel (2012)] using nonconstructive methods that the largest average value of a k x k submatrix is 2(1 + o(1)) root log n/k, with high probability (w.h.p.), when k = O(log n/log log n). In the same paper, evidence was provided that a natural greedy algorithm called the Largest Average Submatrix (LAS) for a constant k shou...
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作者：Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie-Weiss model where we observe the effect of a thermodynamic phase transition. ...
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作者：Fan, Jianqing; Liu, Han; Sun, Qiang; Zhang, Tong
作者单位：Fudan University; Princeton University; Princeton University; University of Toronto
摘要：We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high-dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second...
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作者：Paindaveine, Davy; Van Bever, Germain
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept is similar to those from Chen, Gao and Ren [Robust covariance and scatter matrix estimation under Huber's contamination model (2018)] and Zhang [J. Multivariate Anal. 82 (2002) 134-165]. Rather than focusing, as in these earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so unde...
