Algorithms for estimating spectral sums and matrix approximations
Thursday, April 15, 2021
3:30PM – 5PM
Many modern scientific applications involve large dimensional data matrices, and recent research efforts have focused on developing fast and scalable algorithms for matrix computations. Over the past few years, randomized methods have revolutionized algebraic computation by symbiotizing linear algebra with statistical machinery. In the first part of this talk, we will discuss few novel algorithms for approximating matrix spectral sums (matrix function trace estimation). A number of important matrix properties, including log-determinant, Schatten norms, spectral density, numerical rank, Shannon entropy, and others can all be estimated as spectral sums. The algorithms we discuss, combine randomization techniques with tools from approximation theory to estimate spectral sums faster than the best known runtime for matrix multiplication. We present theoretical analysis and few numerical results to illustrate the performance of these algorithms. In the second part of the talk, we will discuss randomized sketching and sampling algorithms for matrix approximation and data compression. We then present new methods that achieve similar approximation results but with reduced randomness. These methods leverage tools from error correcting codes and sparse graph theory, and we show how they can also be used in other AI applications.
Shashanka Ubaru is a Research Staff Member in the Mathematics of AI group at IBM T.J. Watson Research Center. Previously, he was a Goldstine Postdoctoral Fellow at IBM. Shashanka received his PhD in Computer Science from University of Minnesota. Shashanka's research interests are in Machine Learning, Numerical Linear Algebra, and Coding Theory Applications. In particular, his research work has focused on the use of computational linear algebra tools and error correcting coding theory for solving problems related to machine learning, data analysis and signal processing. Shashanka is a recipient of the IBM Herman Goldstine fellowship and IEEE ICMLA best paper award.