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作者：Kim, Ilmun; Neykov, Matey; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Yonsei University; Carnegie Mellon University
摘要：In this paper, we investigate local permutation tests for testing conditional independence between two random vectors X and Y given Z. The local permutation test determines the significance of a test statistic by locally shuffling samples, which share similar values of the conditioning variables Z, and it forms a natural extension of the usual permutation approach for unconditional independence testing. Despite its simplicity and empirical support, the theoretical underpinnings of the local pe...
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作者：Abbe, Emmanuel; Fan, Jianqing; Wang, Kaizheng
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Princeton University; Columbia University; Columbia University
摘要：Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual principal component scores that yield low-dimensional embedding of samples. That hinders the analysis of various spectral methods. In this paper, we first develop an l(p) perturbation theory for a hollowed version of PCA in Hilbert spaces which...
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作者：Cai, T. Tony; Wei, Hongji
作者单位：University of Pennsylvania
摘要：Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov class, which serves as a benchmark for the cost of adaptation, is established. We then quantify the exact communication cost for adaptation and construct an optimally adaptive procedure for distributed estimation over a range of Besov classes. The results de...
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作者：Dirks, Sjoerd; Maly, Johannes; Rauhut, Holger
作者单位：Utrecht University; University of Munich; RWTH Aachen University
摘要：We consider the classical problem of estimating the covariance matrix of a sub-Gaussian distribution from i.i.d. samples in the novel context of coarse quantization, that is, instead of having full knowledge of the samples, they are quantized to one or two bits per entry. This problem occurs naturally in signal processing applications. We introduce new estimators in two different quantization scenarios and derive nonasymptotic estimation error bounds in terms of the operator norm. In the first...
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作者：Li, Shuangning; Wager, Stefan
作者单位：Stanford University; Stanford University
摘要：The network interference model for treatment effect estimation places experimental units at the vertices of an undirected exposure graph, such that treatment assigned to one unit may affect the outcome of another unit if and only if these two units are connected by an edge. This model has recently gained popularity as means of incorporating interference effects into the Neyman-Rubin potential outcomes framework; and several authors have considered estimation of various causal targets, includin...
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作者：Zhang, Yunyi; Politis, Dimitris N.
作者单位：University of California System; University of California San Diego; University of California System; University of California San Diego
摘要：The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients that are not significant. By contrast, classical ridge regression cannot reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the model selection. As ...
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作者：Han, Rungang; Willett, Rebecca; Zhang, Anru R.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Chicago; University of Chicago
摘要：This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models. To overcome the difficulty of nonconvexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the underlying low-rank stru...
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作者：Jeon, Jeong Min; Park, Byeong U.; Van Keilegom, Ingrid
作者单位：KU Leuven; Seoul National University (SNU)
摘要：This paper develops a foundation of methodology and theory for non-parametric regression with Lie group-valued predictors contaminated by measurement errors. Our methodology and theory are based on harmonic analysis on Lie groups, which is largely unknown in statistics. We establish a novel deconvolution regression estimator, and study its rate of convergence and asymptotic distribution. We also provide asymptotic confidence intervals based on the asymptotic distribution of the estimator and o...
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作者：Lopes, Miles E.
作者单位：University of California System; University of California Davis
摘要：Nonasymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate Kolmogorov distance, in the context of a sum of n random vectors that are p-dimensional and i.i.d. Up to now, a growing line of work has established bounds with mild logarithmic dependence on p. However, the problem of developing corresponding bounds with near n(...
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作者：Montanari, Andrea; Zhong, Yiqiao
作者单位：Stanford University; Stanford University
摘要：Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they achieve good prediction error on unseen data: interpolating the training set does not lead to a large generalization error. Further, overparametrization appears to be beneficial in that it simplifies the optimization landscape. Here, we study these phenomena in t...
