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June, 2022 Convenient Tail Bounds for Sums of Random Tensors
Shih Yu Chang, Wen-Wei Lin
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Taiwanese J. Math. 26(3): 571-606 (June, 2022). DOI: 10.11650/tjm/211201


This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Laplace transform method and Lieb's concavity theorem from matrices to tensors, and apply these tools to generalize the classical bounds associated with the names Chernoff, Bennett, and Bernstein from the scalar to the tensor setting. Tail bounds for the norm of a sum of random rectangular tensors are also derived from corollaries of random Hermitian tensors cases. The proof mechanism can also be applied to tensor-valued martingales and tensor-based Azuma, Hoeffding and McDiarmid inequalities are established.


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Shih Yu Chang. Wen-Wei Lin. "Convenient Tail Bounds for Sums of Random Tensors." Taiwanese J. Math. 26 (3) 571 - 606, June, 2022.


Received: 24 April 2021; Revised: 14 November 2021; Accepted: 2 December 2021; Published: June, 2022
First available in Project Euclid: 12 December 2021

Digital Object Identifier: 10.11650/tjm/211201

Primary: 11M50 , 47A80

Keywords: concentration inequality , Einstein products , Random tensors

Rights: Copyright © 2022 The Mathematical Society of the Republic of China


Vol.26 • No. 3 • June, 2022
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