Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments 被引量：1

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摘要 This paper develops the Bernstein tensor concentration inequality for random tensors of general order,based on the use of Einstein products for tensors.This establishes a strong link between these and matrices,which in turn allows exploitation of existing results for the latter.An interesting application to sample estimators of high-order moments is presented as an illustration.

作者 Ziyan LUO Liqun QI Philippe LTOINT

机构地区 Department of Applied Mathematics Department of Mathematics Department of Applied Mathematics Namur Center for Complex Systems(naXys)

出处《Frontiers of Mathematics in China》 SCIE CSCD 2020年第2期367-384,共18页 中国高等学校学术文摘·数学（英文）

基金 supported by the National Natural Science Foundation of China(Grant No.11771038) the Beijing Natural Science Foundation(Grant No.Z190002) the Hong Kong Research Grant Council(Grant Nos.PolyU 15300715,15301716,15300717)。

关键词 Random tensors concentration inequality Einstein products SUBSAMPLING computational statistics

分类号 O183 [理学—基础数学]

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参考文献1

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共引文献3

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同被引文献1

1Yun Miao,Liqun Qi,Yimin Wei.T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product[J].Communications on Applied Mathematics and Computation,2021,3(2):201-220. 被引量：5

引证文献1

1Shih Yu Chang,Yimin Wei.Generalized T-Product Tensor BernsteinBounds[J].Annals of Applied Mathematics,2022,38(1):25-61.

1Weilin Nie,Cheng Wang.Error Analysis and Variable Selection for Differential Private Learning Algorithm[J].Journal of Applied Mathematics and Physics,2017,5(4):900-911.
2Xinxing WU,Junping ZHANG.Distribution-dependent concentration inequalities for tighter generalization bounds[J].Science China(Information Sciences),2018,61(4):218-220.

Frontiers of Mathematics in China

2020年第2期

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