4 papers
Lasso Universality Under Linearly Dependent Covariates in the Sparse Regime
Soroush Mesforush, Rahul Parhi
Throughout the last decade, Gaussian universality has been widely studied for high-dimensional estimation problems. Most of the literature focuses on i.i.d. sensing matrices or acc…
Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
Tongtong Liang, Esha Singh, Rahul Parhi +2
Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent th…
Towards Sharp Minimax Risk Bounds for Operator Learning
Ben Adcock, Gregor Maier, Rahul Parhi
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples.…
Nonasymptotic Convergence Rates for Plug-and-Play Methods With MMSE Denoisers
Henry Pritchard, Rahul Parhi
It is known that the minimum-mean-squared-error (MMSE) denoiser under Gaussian noise can be written as a proximal operator, which suffices for asymptotic convergence of plug-and-pl…