6 papers
Optimal Recovery Meets Minimax Estimation
Ronald DeVore, Robert D. Nowak, Rahul Parhi +2
A fundamental problem in statistics and machine learning is to estimate a function from possibly noisy observations of its point samples. The goal is to design a numerical algo…
Random ReLU Neural Networks as Non-Gaussian Processes
Rahul Parhi, Pakshal Bohra, Ayoub El Biari +2
We consider a large class of shallow neural networks with randomly initialized parameters and rectified linear unit activation functions. We prove that these random neural networks…
Function-Space Optimality of Neural Architectures with Multivariate Nonlinearities
Rahul Parhi, Michael Unser
We investigate the function-space optimality (specifically, the Banach-space optimality) of a large class of shallow neural architectures with multivariate nonlinearities/activatio…
Weighted variation spaces and approximation by shallow ReLU networks
Ronald DeVore, Robert D. Nowak, Rahul Parhi +1
We investigate the approximation of functions on a bounded domain by the outputs of single-hidden-layer ReLU neural networks of width . This form of…
Variation Spaces for Multi-Output Neural Networks: Insights on Multi-Task Learning and Network Compression
Joseph Shenouda, Rahul Parhi, Kangwook Lee +1
This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of repr…
Distributional Extension and Invertibility of the -Plane Transform and Its Dual
Rahul Parhi, Michael Unser
We investigate the distributional extension of the -plane transform in and of related operators. We parameterize the -plane domain as the Cartesian product of…