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作者：Yang, Yun; Dunson, David B.
作者单位：University of California System; University of California Berkeley; Duke University
摘要：There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors D is large, one encounters a daunting problem in attempting to estimate a D-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a d-dimensional subspace with d << D. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally tractable and theoretically su...
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作者：Perchet, Vianney; Rigollet, Philippe; Chassang, Sylvain; Snowberg, Erik
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Inria; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Princeton University; California Institute of Technology; National Bureau of Economic Research
摘要：Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.
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作者：Bertsimas, Dimitris; King, Angela; Mazumder, Rahul
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing k out of p features in linear regression given n observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as...
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作者：Bhattacharjee, Monika; Bose, Arup
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The existence of limiting spectral distribution (LSD) of (Gamma) over cap (u) + (Gamma) over cap (u)*, the symmetric sum of the sample autocovariance matrix (Gamma) over cap (u) of order u, is known when the observations are from an infinite dimensional vector linear process with appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices such as (Gamma) over cap (u) ...
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作者：Xie, Xianchao; Kou, S. C.; Brown, Lawrence
作者单位：Harvard University; University of Pennsylvania
摘要：This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semiparametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods...
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作者：Liu, Hongcheng; Yao, Tao; Li, Runze
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms ...
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作者：Panaretos, Victor M.; Zemel, Yoav
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random function {Y(x) : x is an element of [0, 1]} corresponds to its random oscillations in the y-axis, typically encapsulated by its (co) variation around a mean level. In contrast, its phase variation refers to fluctuations in the x-axis, often caused by random ti...
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作者：Taylor, Jonathan E.; Loftus, Joshua R.; Tibshirani, Ryan J.
作者单位：Stanford University; Carnegie Mellon University
摘要：We derive an exact p-value for testing a global null hypothesis in a general adaptive regression setting. Our approach uses the Kac-Rice formula [as described in Random Fields and Geometry (2007) Springer, New York] applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, group lasso, principal components and matrix completion problems. For...
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作者：Mukherjee, Sumit
作者单位：Columbia University
摘要：Asymptotics of the normalizing constant are computed for a class of one parameter exponential families on permutations which include Mallows models with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE and a computable approximation of the MLE are shown to be consistent. The pseudo-likelihood estimator of Besag is shown to be root n-consistent. An iterative algorithm (IPFP) is proved to converge to the limiting normalizing constant. The Mallows model with Kendall's tau i...
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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...
