5期

最新文章

• EXACT MINIMAX OPTIMALITY OF SPECTRAL METHODS IN PHASE SYNCHRONIZATION AND ORTHOGONAL GROUP SYNCHRONIZATION AI翻译
  作者：Zhang, Anderson Ye
  作者单位：University of Pennsylvania
  摘要：We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization step. We prove that it achieves the minimax lower bound of the problem with a matching leading constant under a squared 2 pound loss. This shows that the spectral method has the same performance as more sophisticated procedures including maximum likelihood esti...
• JOINT SEQUENTIAL DETECTION AND ISOLATION FOR DEPENDENT DATA STREAMS AI翻译
  作者：Chaudhuri, Anamitra; Fellouris, Georgios
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the oth...
• LEAVE-ONE-OUT SINGULAR SUBSPACE PERTURBATION ANALYSIS FOR SPECTRAL CLUSTERING AI翻译
  作者：Zhang, Anderson Y.; Zhou, Harrison Y.
  作者单位：University of Pennsylvania; Yale University
  摘要：The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out sub- matrix of the other one and establish a novel perturbation upper bound for the distance between the two corresponding singular subspaces. It is well suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds ...
• A GAUSSIAN PROCESS APPROACH TO MODEL CHECKS AI翻译
  作者：Escanciano, Juan Carlos
  作者单位：Universidad Carlos III de Madrid
  摘要：This paper proposes a Gaussian process (GP) approach for testing conditional moment restrictions. Tests are based on squared Neyman orthogonal function-parametric processes integrated with respect to a GP distribution. This methodology leads to a general unified framework of kernel-based tests having the following properties: (i) bootstrap tests are easy to implement in the presence of nuisance parameters (they are simple quadratic forms, and there is no need to reestimate the nuisance paramet...
• WASSERSTEIN GENERATIVE ADVERSARIAL NETWORKS ARE MINIMAX OPTIMAL DISTRIBUTION ESTIMATORS AI翻译
  作者：Stephanovitch, Arthur; Aamari, Eddie; Levrard, Clement
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite de Rennes
  摘要：We provide nonasymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and discriminators which yield a GAN that achieves the minimax optimal rate for estimating a certain probability measure mu with support in Rp. The probability mu is considered to be the push forward of the Lebesgue measure on the d-dimensional torus Td by a map g star : Td -> Rp of smoothness beta + 1. Measuring the err...
• ESTIMATING A DENSITY NEAR AN UNKNOWN MANIFOLD: A BAYESIAN NONPARAMETRIC APPROACH AI翻译
  作者：Berenfeld, Clement; Rosa, Paul; Rousseau, Judith
  作者单位：University of Potsdam; University of Oxford
  摘要：We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic H & ouml;lder for the underlying density and obtain posterior rates that are minimax optimal and adaptive to the regularity of the density, to the intrinsic dimension of the manifold, and to the size of the offset, provided that the latter is not too small-while still allowed to go to zero. Our Bayesian procedure, ...
• GAUSSIAN APPROXIMATION FOR NONSTATIONARY TIME SERIES WITH OPTIMAL RATE AND EXPLICIT CONSTRUCTION AI翻译
  作者：Bonnerjee, Soham; Karmakar, Sayar; Wu, Wei Biao
  作者单位：University of Chicago; State University System of Florida; University of Florida
  摘要：Statistical inference for time series such as curve estimation for time- varying models or testing for existence of a change point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for nonstationary processes only provide an existential proof, and thus they are difficult to apply. In this paper, we provide two clear paths to c...
• COMPUTATIONAL LOWER BOUNDS FOR GRAPHON ESTIMATION VIA LOW-DEGREE POLYNOMIALS AI翻译
  作者：Luo, Yuetian; Gao, Chao
  作者单位：University of Chicago; University of Chicago
  摘要：Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been established by (Ann. Statist. 43 (2015) 2624-2652) for both stochastic block model (SBM) and nonparametric graphon estimation. The statistical optimal estimators are based on constrained least squares and have computational complexity exponential in the dimension. ...
• MULTIVARIATE TREND FILTERING FOR LATTICE DATA AI翻译
  作者：Sadhanala, Veeranjaneyulu; Wang, Yu-xiang; Hu, Addison j.; Tibshirani, Ryan j.
  作者单位：Alphabet Inc.; Google Incorporated; University of California System; University of California San Diego; Carnegie Mellon University; University of California System; University of California Davis
  摘要：We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in d dimensions. KTF is a natural extension of univariate trend filtering ( Int. J. Comput. Vis. 70 (2006) 214-255; SIAM Rev. 51 (2009) 339-360; Ann. Statist. 42 (2014) 285-323), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be estimated along each ...
• TESTING HIGH-DIMENSIONAL REGRESSION COEFFICIENTS IN LINEAR MODELS AI翻译
  作者：Zhao, Alex; Li, Changcheng; Li, Runze; Zhang, Zhe
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Dalian University of Technology
  摘要：This paper is concerned with statistical inference for regression coefficients in high-dimensional linear regression models. We propose a new method for testing the coefficient vector of the high-dimensional linear models, and establish the asymptotic normality of our proposed test statistic with the aid of the martingale central limit theorem. We derive the asymptotical relative efficiency (ARE) of the proposed test with respect to the test proshow that the ARE is always greater or equal to o...