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作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Yichao
作者单位：Southwestern University of Finance & Economics - China; University of Melbourne; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; North Carolina State University
摘要：We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal non...
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作者：Jin, Jiashun; Wang, Wanjie
作者单位：Carnegie Mellon University; National University of Singapore
摘要：We consider a clustering problem where we observe feature vectors X-i is an element of R-P, i = 1, 2,..., n, from K possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the modern regime of p >> n, where classical clustering methods face challenges. We propose Influential Features PCA (IF-PCA) as a new clustering procedure. In IF-PCA, we select a small fraction of features with the largest Kolmogorov Smirnov (KS) scores, obtai...
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作者：Stepanova, Natalia A.; Tsybakov, Alexandre B.
作者单位：Carleton University; Institut Polytechnique de Paris; ENSAE Paris
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作者：Karwa, Vishesh; Slavkovic, Aleksandra
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The beta-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the beta-model, and show that the MLE never exists for the degree partition beta-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of beta-model, a...
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作者：Devroye, Luc; Lerasle, Matthieu; Lugosi, Gabor; Olivetra, Roberto I.
作者单位：McGill University; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Pompeu Fabra University
摘要：We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.
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作者：Hayashi, Masahito; Watanabe, Shun
作者单位：Nagoya University; National University of Singapore; Tokyo University of Agriculture & Technology
摘要：We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then we show that the sample mean of the generator of the exponential family is an asymptotically efficient estimator. Further, we also define a curved exponential family of transition matrices. Using a transition matrix version of the Pythagorean theorem, we give an asymptotically efficient estimator for a curved exponential family.
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作者：Lam, Clifford
作者单位：University of London; London School Economics & Political Science
摘要：We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size...
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作者：Cai, T. Tony; Liu, Weidong; Zhou, Harrison H.
作者单位：University of Pennsylvania; Shanghai Jiao Tong University; Shanghai Jiao Tong University; Yale University
摘要：Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained l(1) minimization is proposed and its rate of convergence is obtained over a collection of parameter spaces. The estimator, called ACLIME, is e...
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作者：Cai, Tony; Kim, Donggyu; Wang, Yazhen; Yuan, Ming; Zhou, Harrison H.
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison; Yale University
摘要：Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions, for a proof of its...
