The Hanson-Wright Inequality for Random Tensors

2021/06/24 by Bamberger, Stefan, Krahmer, Felix, Ward, Rachel
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2106.13345

Abstract

We provide moment bounds for expressions of the type (X⁽¹⁾ ⊗ … ⊗ X^(d))^T A (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.

Related

• Generalized Hanson-Wright Inequality for Random Tensors
• Concentration inequalities for random tensors
• Hanson-Wright Inequality for Random Tensors under Einstein Product
• Uniform Hanson-Wright type concentration inequalities for unbounded\n entries via the entropy method
• Anticoncentration and Berry--Esseen bounds for random tensors