We review randomized algorithms for the numerical solution of least squares/regression problems, with a focus on algorithms that row-sketch from the left, or column-sketch from the right. These algorithms tend to be efficient and accurate on matrices that have many more rows than columns. We present probabilistic bounds for the amount of sampling required to achieve a user-specified error tolerance; and discuss the effect of sampling on the underlying Gaussian linear model in regression problems. Numerical experiments illustrate that the bounds are informative even for small problem dimensions and stringent success probabilities.

This talk is accessible to graduate students.

Ilse Ipsen received a Bachelor’s degree from the University of Kaiserslautern in Germany and a Ph.D. from Penn State, both in Computer Science. She taught Computer Science at Yale for 10 years, and is now Professor of Mathematics at NC State, with affiliate appointments in Statistics and the Institute for Advanced Analytics. Her research interests include numerical linear algebra, randomized algorithms, and probabilistic numerics; and she has authored a graduate text book on Numerical Matrix Analysis.

Ilse Ipsen is the founding Editor-in-Chief of the SIAM Book Series on Data Science and serves on the editorial boards of SIAM Review, Numerische Mathematik, and Acta Numerica. She has been SIAM Vice-President for Programs, SIAM Vice-President at Large, and Associate Director of SAMSI. She is a Fellow of the AAAS and SIAM.

Contact the host, Dmitry Zenkov for the zoom link.