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作者：Jiao, Yuling; Shen, Guohao; Liu, Yuanyuan; Huang, Jian
作者单位：Wuhan University; Hong Kong Polytechnic University; Chinese University of Hong Kong
摘要：We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the exist-ing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent the curse of dime...
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作者：Li, Mengchu; Berrett, Thomas B.; Yu, Yi
作者单位：University of Warwick
摘要：It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local dif-ferential privacy (LDP) constraints.In this paper, we start with a general minimax lower bound result, which di...
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作者：Buecher, Axel; Zanger, Leandra
作者单位：Heinrich Heine University Dusseldorf
摘要：Modeling univariate block maxima by the generalized extreme value dis-tribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying station-ary time series, respective estimators may be improved by calculating block maxima in an overlapping way. A proof of concept is provided that the lat-ter finding also holds in situations that involve certain piecewise stationari-ties. A weak convergence result for an empirica...
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作者：Schell, Alexander; Oberhauser, Harald
作者单位：University of Oxford
摘要：We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with 'non-degenerate' second-order statistics. The lat...
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作者：Reiss, Markus; Winkelmann, Lars
作者单位：Humboldt University of Berlin; Free University of Berlin
摘要：We study the rank of the instantaneous or spot covariance matrix ⠂X (t) of a multidimensional process X (t). Given high-frequency observations X(i/n), i = 0, ... , n, we test the null hypothesis rank(⠂X(t)) & LE; r for all t against local alternatives where the average (r + 1)st eigenvalue is larger than some signal detection rate vn. A major problem is that the inherent averaging in local covariance statistics produces a bias that distorts the rank statistics. We show that the bias depends ...
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作者：Abbe, Emmanuel; Li, Shuangping; Sly, Allan
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Princeton University; Princeton University
摘要：The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the re-cent years in sparser regimes. Yet, the current techniques still require diverg-ing degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper pro-vides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succe...
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作者：Lyu, Zhongyuan; Xia, Dong
作者单位：Hong Kong University of Science & Technology
摘要：Structural matrix-variate observations routinely arise in diverse fields such as multilayer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the fundamental questions like its statistical optimality and computational limit are largely under-explored. In this paper, we propose a low-rank Gaussian mixture model (LrMM) assuming each matrix-valued observation has a planted low-rank structure. Minimax low...
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作者：Wang, Di; Tsay, Ruey S.
作者单位：Shanghai Jiao Tong University; University of Chicago
摘要：High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is robust to model mi...
