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作者：Huang, Jianhua Z.; Su, Ya
作者单位：Texas A&M University System; Texas A&M University College Station; Virginia Commonwealth University
摘要：This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the asymptotic behaviors of th...
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作者：She, Yiyuan; Wang, Zhifeng; Jin, Jiuwu
作者单位：State University System of Florida; Florida State University
摘要：Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for nonconvex and nonsmooth o...
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作者：Hirshberg, David A.; Wager, Stefan
作者单位：Stanford University
摘要：Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plugin estimator by subtracting a minimax linear...
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作者：Jing, Bing-Yi; Li, Ting; Lyu, Zhongyuan; Xia, Dong
作者单位：Hong Kong University of Science & Technology; Hong Kong Polytechnic University
摘要：We study the problem of community detection in multilayer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, that is, mixture multilayer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification er...
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作者：Castillo, Ismael; Rockova, Veronika
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; University of Chicago
摘要：This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. The practically used Bayesian CART priors are shown to attain adaptive near rate-minimax posterior concentration in the supremum norm in regression mo...
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作者：Hamm, Thomas; Steinwart, Ingo
作者单位：University of Stuttgart
摘要：We derive improved regression and classification rates for support vector machines using Gaussian kernels under the assumption that the data has some low-dimensional intrinsic structure that is described by the box-counting dimension. Under some standard regularity assumptions for regression and classification, we prove learning rates, in which the dimension of the ambient space is replaced by the box-counting dimension of the support of the data generating distribution. In the regression case...
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作者：Manole, Tudor; Khalili, Abbas
作者单位：Carnegie Mellon University; McGill University
摘要：Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure-a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model pa...
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作者：Mukherjee, Debarghya; Banerjee, Moulinath; Ritov, Ya'acov
作者单位：University of Michigan System; University of Michigan
摘要：Manski's celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under growing dimension scenarios largely remains unknown. This paper addresses that gap. Two different cases are considered: p grows with n but at a slow rate, that is, p / n -> 0; and p >> n (fast growth). In the binary response model, we recast Manski's score estimat...
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作者：Reeve, Henry W. J.; Cannings, Timothy, I; Samworth, Richard J.
作者单位：University of Bristol; University of Edinburgh; University of Cambridge
摘要：In transfer learning, we wish to make inference about a target population when we have access to data both from the distribution itself, and from a different but related source distribution. We introduce a flexible framework for transfer learning in the context of binary classification, allowing for covariate-dependent relationships between the source and target distributions that are not required to preserve the Bayes decision boundary. Our main contributions are to derive the minimax optimal...
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作者：Gerber, Mathieu; Heine, Kari
作者单位：University of Bristol; University of Bath
摘要：Let (Y-t)(t >= 1) be a sequence of i.i.d. observations and {f(theta), theta is an element of R-d} be a parametric model. We introduce a new online algorithm for computing a sequence ((theta) over cap (t))(t >= 1), which is shown to converge almost surely to argmax(theta is an element of Rd) E[log f(theta)(Y-1)] at rate O(log(t)((1+epsilon)/2t-1/2)), with epsilon > 0 a user specified parameter. This convergence result is obtained under standard conditions on the statistical model and, most nota...
