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 i...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.展开更多
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)。
文摘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.
