10 papers
Linear Time Kernel Matrix Approximation via Hyperspherical Harmonics
John Paul Ryan, Anil Damle
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically construc…
Selected Columns of the Density Matrix in an Atomic Orbital Basis I: An Intrinsic and Non-Iterative Orbital Localization Scheme for the Occupied Space
Eric G. Fuemmeler, Anil Damle, Robert A. DiStasio
We extend the selected columns of the density matrix (SCDM) methodology [J. Chem. Theory Comput. 2015, 11, 1463--1469]---a non-iterative procedure for generating localized occupied…
The Fast Kernel Transform
John Paul Ryan, Sebastian Ament, Carla P. Gomes +1
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations invo…
Over-parametrized neural networks as under-determined linear systems
Austin R. Benson, Anil Damle, Alex Townsend
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural n…
Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization
Geoff Pleiss, Martin Jankowiak, David Eriksson +2
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians or whitening a…
Entrywise convergence of iterative methods for eigenproblems
Vasileios Charisopoulos, Austin R. Benson, Anil Damle
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically perf…