5 papers
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Beyond Expectation: Concentration Inequalities for Randomized Iterative Methods
Toby Anderson, Max Collins, Jamie Haddock +2
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprin…
Subspace-constrained randomized coordinate descent for linear systems with good low-rank matrix approximations
Jackie Lok, Elizaveta Rebrova
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the sol…
On Regularization via Early Stopping for Least Squares Regression
Rishi Sonthalia, Jackie Lok, Elizaveta Rebrova
A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear…
Error dynamics of mini-batch gradient descent with random reshuffling for least squares regression
Jackie Lok, Rishi Sonthalia, Elizaveta Rebrova
We study the discrete dynamics of mini-batch gradient descent with random reshuffling for least squares regression. We show that the training and generalization errors depend on a…