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作者：Qiu, Rui; Xu, Shuntuo; Yu, Zhou
作者单位：East China Normal University
摘要：Neural networks and random forests are popular and promising tools for machine learning. This article explores the proper integration of these two approaches for nonparametric regression to improve the performance of a single approach. Specifically, we propose a neural network estimator with local enhancement provided by random forests. It naturally synthesizes the local relation adaptivity of random forests and the strong global approximation ability of neural networks. Based on the classical...
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作者：Tan, Jianbin; Zhang, Guoyu; Wang, Xueqin; Huang, Hui; Yao, Fang
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Sun Yat Sen University; Peking University; Renmin University of China
摘要：Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green's matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate trajectories in dynamic systems...
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作者：Zhou, Ya; Wong, Raymond K. W.; He, Kejun
作者单位：Renmin University of China; Texas A&M University System; Texas A&M University College Station; Renmin University of China
摘要：We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate. We also provide a minimax lower bound, which characterizes th...
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作者：Catalano, Marta; Fasano, Augusto; Rebaudo, Giovanni
作者单位：University of Warwick; University of Turin
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作者：Greenland, Sander
作者单位：University of California System; University of California Los Angeles; University of California System; University of California Los Angeles
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作者：Gruenwald, Peter; de Heide, Rianne; Koolen, Wouter
作者单位：Leiden University - Excl LUMC; Leiden University; Vrije Universiteit Amsterdam; University of Twente
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作者：Xu, Wenkai
作者单位：Eberhard Karls University of Tubingen
摘要：We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values are safe, i.e. they preserve type-I error guarantees, under such optional continuation. We define growth rate optimality (GRO) as an analogue of power in an optional continuation context, and we show ...
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作者：ter Schure, Judith
作者单位：University of Amsterdam
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作者：Han, Yuefeng; Yang, Dan; Zhang, Cun-Hui; Chen, Rong
作者单位：University of Notre Dame; University of Hong Kong; Rutgers University System; Rutgers University New Brunswick
摘要：Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tenso...
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作者：Gu, Jiaqi; Yin, Guosheng
作者单位：Stanford University; Imperial College London; Stanford University
