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作者：Koltchinskii, Vladimir; Lounici, Karim
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let X, X-1,...,X-n be i.i.d. Gaussian random variables in a separable Hilbert space H with zero mean and covariance operator Sigma = E(X circle times X), and let (Sigma) over cap := n(-1) Sigma(n)(j=1) (X-i circle times X-j) be the sample (empirical) covariance operator based on (XI,..,Xn). Denote by P-r the spectral projector of Sigma corresponding to its rth eigenvalue mu(r) and by (P-r) over cap the empirical counterpart of P-r. The main goal of the paper is to obtain tight bounds on sup(x ...
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作者：Ghoshdastidar, Debarghya; Dukkipati, Ambedkar
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under t...
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作者：Ning, Yang; Liu, Han
作者单位：Cornell University; Princeton University
摘要：We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a novel decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high dimensional inference and is applicable t...
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作者：Wang, Qinwen; Yao, Jianfeng
作者单位：University of Hong Kong
摘要：Consider two p-variate populations, not necessarily Gaussian, with covariance matrices Sigma 1 and Sigma 2, respectively. Let S-1 and S-2 be the corresponding sample covariance matrices with degrees of freedom m and n. When the difference Delta between Sigma l and Sigma 2 is of small rank compared to p, m and n, the Fisher matrix S := S2-1S1 is called a spiked Fisher matrix. When p, m and n grow to infinity proportionally, we establish a phase transition for the extreme eigenvalues of the Fish...
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作者：Belloni, Alexandre; Oliveira, Roberto I.
作者单位：Duke University; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial (ss)-mixing. In particular, model misspecification...
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作者：Balakrishnan, Sivaraman; Wainwrightt, Martin J.; Yu, Bin
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University
摘要：The EM algorithm is a widely used tool in maximum-likelihood estimation in incomplete data problems. Existing theoretical work has focused on conditions under which the iterates or likelihood values converge, and the associated rates of convergence. Such guarantees do not distinguish whether the ultimate fixed point is a near global optimum or a bad local optimum of the sample likelihood, nor do they relate the obtained fixed point to the global optima of the idealized population likelihood (o...
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作者：Klopp, Olga; Tsybakov, Alexandre B.; Verzelen, Nicolas
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Institut Polytechnique de Paris; ENSAE Paris; INRAE
摘要：Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. Taking the stochastic block model as an approximation, we construct estimators of network connection probabilities the ordinary block constant least squares estimator, and its restricted version. We show that they sa...
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作者：Chernozhukov, Victor; Hansen, Christian; Liao, Yuan
作者单位：Massachusetts Institute of Technology (MIT); University of Chicago; University System of Maryland; University of Maryland College Park
摘要：Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of nonzero parameters that are large in magnitude, or a dense signal model, a model with no large parameters and very many small nonzero parameters. We consider a generalization of these two basic models, termed here a sparse + dense model, in which the signal is given by the sum of a sparse signal and a dense signal. Such a structur...
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作者：Khare, Kshitij; Pal, Subhadip; Su, Zhihua
作者单位：State University System of Florida; University of Florida
摘要：The envelope model is a new paradigm to address estimation and prediction in multivariate analysis. Using sufficient dimension reduction techniques, it has the potential to achieve substantial efficiency gains compared to standard models. This model was first introduced by [Statist. Sinica 20 (2010) 927-960] for multivariate linear regression, and has since been adapted to many other contexts. However, a Bayesian approach for analyzing envelope models has not yet been investigated in the liter...
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作者：Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.
作者单位：Duke University; Texas A&M University System; Texas A&M University College Station
摘要：Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support ...
