-
作者：Uhler, Caroline; Lenkoski, Alex; Richards, Donald
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate prior for inverse covariance matrices satisfying graphical constraints. While it is straightforward to posit the unnormalized densities, the normalizing constants of these distributions have been known only for graphs that are chordal, or decomposable. Up until ...
-
作者：Pretorius, Charl; Swanepoel, Jan W. H.
作者单位：North West University - South Africa
摘要：We propose a new method, based on sample splitting, for constructing bootstrap confidence bounds for a parameter appearing in the regular smooth function model. It has been demonstrated in the literature, for example, by Hall [Ann. Statist. 16 (1988) 927-985; The Bootstrap and Edgeworth Expansion (1992) Springer], that the well-known percentile-t method for constructing bootstrap confidence bounds typically incurs a coverage error of order O(n(-1)), with n being the sample size. Our version of...
-
作者：Rockova, Veronika
作者单位：University of Chicago
摘要：We introduce a new framework for estimation of sparse normal means, bridging the gap between popular frequentist strategies (LASSO) and popular Bayesian strategies (spike-and-slab). The main thrust of this paper is to introduce the family of Spike-and-Slab LASSO (SS-LASSO) priors, which form a continuum between the Laplace prior and the point-mass spike-and-slab prior. We establish several appealing frequentist properties of SS-LASSO priors, contrasting them with these two limiting cases. Firs...
-
作者：Seo, Myung Hwan; Otsu, Taisuke
作者单位：Seoul National University (SNU); University of London; London School Economics & Political Science
摘要：We examine the asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, the conditional maximum score estimator for a panel data discrete choice model and many other widely used estimators in statistics and econometrics. Specifically, they allow for discontinuous criterion functions of weakly dependent observations which may be localized by kernel smoothing and contain nuisanc...
-
作者：Cai, T. Tony; Zhang, Anru
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison
摘要：Perturbation bounds for singular spaces, in particularWedin's sin Theta theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius sin Theta distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rate-optimal, are also given. The new perturbation bounds are appli...
-
作者：Lin, Zhenhua; Mueller, Hans-Georg; Yao, Fang
作者单位：University of Toronto; University of California System; University of California Davis; Peking University
摘要：We introduce the concept of mixture inner product spaces associated with a given separable Hilbert space, which feature an infinite-dimensional mixture of finite-dimensional vector spaces and are dense in the underlying Hilbert space. Any Hilbert valued random element can be arbitrarily closely approximated by mixture inner product space valued random elements. While this concept can be applied to data in any infinite-dimensional Hilbert space, the case of functional data that are random eleme...
-
作者：Zhao, Tuo; Liu, Han; Zhang, Tong
作者单位：University System of Georgia; Georgia Institute of Technology; Princeton University; Tencent
摘要：The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: warm start initialization, active set updating and strong rule for coordinate preselection. Such a complex algorithmic structure grants superior empirical performance, but also poses significant challenge to theoretical analysis. To tackle this lo...
-
作者：Amini, Arash A.; Levina, Elizaveta
作者单位：University of California System; University of California Los Angeles; University of Michigan System; University of Michigan
摘要：The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. We put ours and previously proposed SDPs in a unified framework, as relaxations of the MLE over various subclasses of the SBM, which also reveals a connection to the well-known pr...
-
作者：Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Columbia University
摘要：The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered [In Proc. 4th Berkeley Sympos. Math. Statist. and Prob. (1961) 105-123; J. Roy. Statist. Soc. Ser. B 24 (1962) 406-424]. The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ra...
-
作者：Dobriban, Edgar; Wager, Stefan
作者单位：University of Pennsylvania; Stanford University
摘要：We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where p, n -> infinity and p/n -> gamma > 0, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance matrix, the signal strength and ...
