4 papers
Exact Spectral Uncertainty Decomposition for Linear-Gaussian Bayesian M/EEG Inverse Problems
Ismail Huseynov, Stefan Haufe
Distributed magneto- and electroencephalographic (M/EEG) source reconstruction is a severely underdetermined linear inverse problem. Bayesian source imaging regularizes inversion t…
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
Arzu Ahmadova, Ismail Huseynov
We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided Hölder regularity. Unlike classical Hölder- or Lipschitz-gradient…
Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds
Ismail Huseynov, Arzu Ahmadova, Agamirza Bashirov
Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous \emph{a posteriori} up…
Structure-Preserving Correction Learning for Sparse Bayesian Inference in Brain Source Imaging
Marco Morik, Xiao Ruiting, Shinichi Nakajima +2
Classical sparse Type-II Bayesian methods for M/EEG brain imaging support joint estimation of source and noise hyperparameters, but rely on fixed iterative update rules. Although t…