2013

最新文章

• STRUCTURE ESTIMATION FOR DISCRETE GRAPHICAL MODELS: GENERALIZED COVARIANCE MATRICES AND THEIR INVERSES AI翻译
  作者：Loh, Po-Ling; Wainwright, Martin J.
  作者单位：University of California System; University of California Berkeley
  摘要：We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an...
• CONVERGENCE RATES OF EIGENVECTOR EMPIRICAL SPECTRAL DISTRIBUTION OF LARGE DIMENSIONAL SAMPLE COVARIANCE MATRIX AI翻译
  作者：Xia, Ningning; Qin, Yingli; Bai, Zhidong
  作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; University of Waterloo
  摘要：The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Marcenko-Pastur distribution function is of order O(N-1/2). Given that data dimension n to sample size N ratio is bounded between 0 and 1, this convergence rate is established under finite 10th moment condition of the u...
• ASYMPTOTIC THEORY WITH HIERARCHICAL AUTO CORRELATION: ORNSTEIN-UHLENBECK TREE MODELS AI翻译
  作者：Ho, Lam Si Tung; Ane, Cecile
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When observations are modeled using an Ornstein-Uhlenbeck (OU) process along the tree, the autocorrelation between two tips decreases exponentially with their tree distance. These models are most often applied in evolutionary biology, when tips represent biological specie...
• ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD AND ITS VARIATIONAL APPROXIMATION FOR STOCHASTIC BLOCKMODELS AI翻译
  作者：Bickel, Peter; Choi, David; Chang, Xiangyu; Zhang, Hai
  作者单位：University of California System; University of California Berkeley; Carnegie Mellon University; Xi'an Jiaotong University; Northwest University Xi'an
  摘要：Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.
• QUANTUM LOCAL ASYMPTOTIC NORMALITY BASED ON A NEW QUANTUM LIKELIHOOD RATIO AI翻译
  作者：Yamagata, Koichi; Fujiwara, Akio; Gill, Richard D.
  作者单位：University of Osaka; Leiden University - Excl LUMC; Leiden University
  摘要：We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.
• MOMENT BOUNDS AND MEAN SQUARED PREDICTION ERRORS OF LONG-MEMORY TIME SERIES AI翻译
  作者：Chan, Ngai Hang; Huang, Shih-Feng; Ing, Ching-Kang
  作者单位：Chinese University of Hong Kong; National University Kaohsiung; Academia Sinica - Taiwan
  摘要：A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction errors (MSPE) of the...
• LOCAL AND GLOBAL ASYMPTOTIC INFERENCE IN SMOOTHING SPLINE MODELS AI翻译
  作者：Shang, Zuofeng; Cheng, Guang
  作者单位：University of Notre Dame; Purdue University System; Purdue University
  摘要：This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577-580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii) local likelihood ratio...
• DENSITY-SENSITIVE SEMISUPERVISED INFERENCE AI翻译
  作者：Azizyan, Martin; Singh, Aarti; Wasserman, Larry
  作者单位：Carnegie Mellon University; Carnegie Mellon University
  摘要：Semisupervised methods are techniques for using labeled data (X-1, Y-1), ..., (X-n, Y-n) together with unlabeled data Xn+1, ..., X-N to make predictions. These methods invoke some assumptions that link the marginal distribution P-X of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of P-X. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a m...
• THE MULTI-ARMED BANDIT PROBLEM WITH COVARIATES AI翻译
  作者：Perchet, Vianney; Rigollet, Philippe
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Princeton University
  摘要：We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side information is available We adopt a nonparametric model where the expected rewards are smooth functions of the covariate and where the hardness of the problem is captured by a margi...
• OPTIMAL CLASSIFICATION IN SPARSE GAUSSIAN GRAPHIC MODEL AI翻译
  作者：Fan, Yingying; Jin, Jiashun; Yao, Zhigang
  作者单位：University of Southern California; Carnegie Mellon University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix Sigma, where the precision matrix Omega = Sigma(-1) is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of Omega, we formulate the setting as a linear regre...