Convenient Tail Bounds for Sums of Random Tensors

Shih Yu Chang*, Wen Wei Lin

*此作品的通信作者

研究成果: Article同行評審

摘要

This work prepares new probability bounds for sums of random, inde-pendent, 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, Ben-nett, 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 es-tablished.

原文English
頁(從 - 到)571-606
頁數36
期刊Taiwanese Journal of Mathematics
26
發行號3
DOIs
出版狀態Published - 6月 2022

指紋

深入研究「Convenient Tail Bounds for Sums of Random Tensors」主題。共同形成了獨特的指紋。

引用此