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…
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…
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.…