Statistics meets optimization: Rigorous guarantees for solving nonconvex programs

12noon lunch and discussion for students, grad students and postdocs¿Perspectives in Machine Learning¿3:30pm Seminar and reception In this talk, we discuss a framework for establishing rigorous results for different types of nonconvex optimization problems that arise in statistical machine learning. Nonconvex optimization is known to be intractable in the general setting. However, problems arising in machine learning are not adversarially constructed, but rather related to a population oracle problem that can be well-behaved. We discuss how this intuition can be made precise for a number of different problems, including high-dimensional sparse regression with nonconvex regularization, as well as various applications of the EM algorithm to latent variable models with nonconvex likelihoods.Based on joint work with Sivaraman Balakrishnan, Po-Ling Loh and Bin Yu.BiographyMartin Wainwright is currently a professor at University of California at Berkeley, with a joint appointment between the Department of Statistics and the Department of Electrical Engineering and Computer Sciences (EECS). He received a Bachelor's degree in Mathematics from University of Waterloo, Canada, and Ph.D. degree in EECS from Massachusetts Institute of Technology (MIT). His research interests include high-dimensional statistics, information theory, statistical machine learning, and optimization theory.