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Stochastic Rounding Implicitly Regularizes Tall-and-Thin Matrices
Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows than columns.
Probabilistic Iterative Methods for Linear Systems
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$.
A Projector-Based Approach to Quantifying Total and Excess Uncertainties for Sketched Linear Regression
To answer this question, we present a projector-based approach to sketched linear regression that is exact and that requires minimal assumptions on the sketching matrix.
Randomized Approximation of the Gram Matrix: Exact Computation and Probabilistic Bounds
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A.
