Talk Summary: Many empirical questions about machine learning systems are best answered through the eigenvalues of associated matrices.  For example, the Hessian of the loss function for a large deep network gives us insight into the difficulty of optimization and sensitivity to parameters.  The spectra of adjacency and Laplacian matrices of large graphs helps us understand the global structure between vertices.  Unfortunately, in the most interesting situations, these matrices are too large to be explicitly instantiated, to say nothing of diagonalizing them directly; rather they are implicit matrices, which can only be interrogated via matrix-vector products.  In this talk, we will discuss how several different randomized estimation tricks can be assembled to construct unbiased estimators of the spectra of large implicit matrices via generalized traces and provide analysis of an interesting use case. This is an adaption of a talk given by Ryan Adams (Harvard University) at Simons Institute for Theory of Computing.

Speaker Bio: Christopher Harshaw is a 2nd year PhD student in the Computer Science department, where he is advised by Daniel Spielman and Amin Karbasi. His research interests are in spectral graph theory, numerical linear algebra, submodular optimization, and applications to machine learning. He is generally interested in the interplay between continuous and discrete optimization and enjoys being a part of the YINS community. Christopher has one of the top ten fastest plasma car race times within the YINS community and is going for the gold this upcoming fall semester.