TY - JOUR
T1 - The Hanson–Wright inequality for random tensors
AU - Bamberger, Stefan
AU - Krahmer, Felix
AU - Ward, Rachel
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12
Y1 - 2022/12
N2 - We provide moment bounds for expressions of the type (X(1)⊗⋯⊗X(d))TA(X(1)⊗⋯⊗X(d)) where ⊗ denotes the Kronecker product and X(1), … , X(d) are random vectors with independent, mean 0, variance 1, subgaussian entries. The bounds are tight up to constants depending on d for the case of Gaussian random vectors. Our proof also provides a decoupling inequality for expressions of this type. Using these bounds, we obtain new, improved concentration inequalities for expressions of the form ‖ B(X(1)⊗ ⋯ ⊗ X(d)) ‖ 2.
AB - We provide moment bounds for expressions of the type (X(1)⊗⋯⊗X(d))TA(X(1)⊗⋯⊗X(d)) where ⊗ denotes the Kronecker product and X(1), … , X(d) are random vectors with independent, mean 0, variance 1, subgaussian entries. The bounds are tight up to constants depending on d for the case of Gaussian random vectors. Our proof also provides a decoupling inequality for expressions of this type. Using these bounds, we obtain new, improved concentration inequalities for expressions of the form ‖ B(X(1)⊗ ⋯ ⊗ X(d)) ‖ 2.
KW - Hanson–Wright inequality
KW - Kronecker product
KW - Random tensors
KW - Subgaussian random variables
UR - http://www.scopus.com/inward/record.url?scp=85135276242&partnerID=8YFLogxK
U2 - 10.1007/s43670-022-00028-4
DO - 10.1007/s43670-022-00028-4
M3 - Article
AN - SCOPUS:85135276242
SN - 2730-5716
VL - 20
JO - Sampling Theory, Signal Processing, and Data Analysis
JF - Sampling Theory, Signal Processing, and Data Analysis
IS - 2
M1 - 14
ER -