Resilience of the quadratic Littlewood-Offord problem

arXiv:2402.10504v1 Announce Type: cross
Abstract: We study the statistical resilience of high-dimensional data. Our results provide estimates as to the effects of adversarial noise over the anti-concentration properties of the quadratic Radamecher chaos $\boldsymbol{\xi}^{\mathsf{T}} M \boldsymbol{\xi}$, where $M$ is a fixed (high-dimensional) matrix and $\boldsymbol{\xi}$ is a conformal Rademacher vector. Specifically, we pursue the question of how many adversarial sign-flips can $\boldsymbol{\xi}$ sustain without "inflating" $\sup_{x\in \mathbb{R}} \mathbb{P} \left\{\boldsymbol{\xi}^{\mathsf{T}} M \boldsymbol{\xi} = x\right\}$ and thus "de-smooth" the original distribution resulting …

abstract adversarial arxiv chaos cs.it cs.lg data effects math.co math.it math.pr matrix noise resilience statistical stat.ml study type vector