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作者：Zhang, Lu; Lu, Junwei
作者单位：Harvard University; Harvard University
摘要：Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high-dimensional graphical models and control the false discovery rat...
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作者：Cai, T. Tony; Chen, Ran; Zhu, Yuancheng
作者单位：University of Pennsylvania
摘要：Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for the minimizer and ...
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作者：Duchi, John C.; Ruan, Feng
作者单位：Stanford University; Northwestern University
摘要：We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning problems by developing the local minimax risk. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to evaluate the difficulty of individual problem instances and delineate the possibilities for adaptation in private...
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作者：Dudeja, Rishabh; Hsu, Daniel
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA exhibits a statistical-computational gap, that is, a sample size regime where the problem is information-theoretically solvable but conjectured to be computationally hard. This paper derives computational lower bounds on the run -time of memory bounded algor...
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作者：Cai, Changxiao; Cai, T. Tony; Li, Hongzhe
作者单位：University of Michigan System; University of Michigan; University of Pennsylvania; University of Pennsylvania
摘要：Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected from source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the data from the source d...
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作者：Ohn, Ilsang; Lin, Lizhen
作者单位：Inha University; University System of Maryland; University of Maryland College Park
摘要：In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally tractable variational Bayes method that performs adaptive inference. To fill this gap, we propose a novel adaptive variational Bayes framework, which can operate on a collection of models. The proposed framework first computes a variational posterior over each...
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作者：Fan, Zhou; Lederman, Roy R.; Sun, Yi; Wang, Tianhao; Xu, Sheng
作者单位：Yale University; University of Chicago
摘要：Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the loglikelihood landscape to a sequence of moment ...
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作者：Schmidt-Hieber, Johannes; Vu, Don
作者单位：University of Twente; Vrije Universiteit Amsterdam
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作者：Chen, Weilin; Lam, Clifford
作者单位：University of London; London School Economics & Political Science
摘要：The idiosyncratic components of a tensor time series factor model can exhibit serial correlations, (e.g., finance or economic data), ruling out many ponents. While the traditional higher order orthogonal iteration (HOOI) is proved to be convergent to a set of factor loading matrices, the closeness of them to the true underlying factor loading matrices are in general not established, or only under i.i.d. Gaussian noises. Under the presence of serial and cross-correlations in the idiosyncratic c...
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作者：Dou, Zehao; Fan, Zhou; Zhou, Harrison H.
作者单位：Yale University
摘要：We study the continuous multireference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryoelectron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K. In a high-noise regime with noise variance sigma 2 >= K, for signals with Fourier coefficients of roughly uniform magnitude, the rate scales as sigma 6 and has no ...
