Analysis of Neural Fragility: Bounding the Norm of a Rank-One Perturbation Matrix
Over 15 million epilepsy patients worldwide do not respond to drugs and require surgical treatment. Successful surgical treatment requires complete removal, or disconnection of the epileptogenic zone (EZ), but without a prospective biomarker of the EZ, surgical success rates vary between 30%-70%. Neural fragility is a model recently proposed to localize the EZ. Neural fragility is computed as the l2 norm of a structured rank-one perturbation of an estimated linear dynamical system. However, an analysis of its numerical properties have not been explored. We show that neural fragility is a well-defined model given a good estimator of the linear dynamical system from data. Specifically, we provide bounds on neural fragility as a function of the underlying linear system and noise.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Antifragility as a complex system's response to perturbations, volatility, and time
Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system's output response to input va…
The Sup-norm Perturbation of HOSVD and Low Rank Tensor Denoising
The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial…
ClusteringDenoisingMarket Fragility, Systemic Risk, and Ricci Curvature
Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have…
Stocks and Cryptocurrencies: Anti-fragile or Robust?
In contrast with robust systems that resist noise or fragile systems that break with noise, antifragility is defined as a property of complex systems that benefit from noise or disorder. Here we define and test a simple …
Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacy
A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private …