Oct 14, 2016
Lopata Hall, Room 101
Sketching as a Tool for Linear Algebra
David Woodruff, Research Scientist, IBM Almaden Research Center
We give near optimal algorithms for regression, low rank approximation, and robust variants of these problems. Our results are based on the sketch and solve paradigm, which is a tool for quickly compressing a problem to a smaller version of itself, for which one can then run a slow algorithm on the smaller problem. These lead to the fastest known algorithms for fundamental machine learning and numerical linear algebra problems, which run in time proportional to the number of non-zero entries of the input. We first give algorithms for least squares regression, and robust variants such as l_p regression and M-Estimator loss functions. Then we give algorithms for approximate singular value decomposition, and robust variants such as minimizing sum of distances to a subspace, rather than sum of squared distances.
David Woodruff joined IBM Almaden Research Center in 2007 right after completing his Ph.D. at MIT in theoretical computer science. He has been at IBM Almaden ever since. His research interests include communication complexity, data stream algorithms, machine learning, numerical linear algebra, sketching, and sparse recovery. He is the recipient of the 2014 Presburger Award and Best Paper Awards at STOC 2013 and PODS 2010. At IBM he is a member of the Academy of Technology and a Master Inventor.