The Landscape of Some Statistical Problems

Wednesday, April 19, 2017 - 4:30pm

Speaker Name

Andrea Montanari

Affiliation

Stanford University

Building and Room number

2-190

Abstract

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point (each example). Studying the landscape of the empirical risk is useful to understand the computational complexity of these statistical problems. I will discuss some generic features that can be used to prove that the global minimizer can be computed efficiently even if the loss in non-convex. A different mechanism arises in some rank-constrained semidefinite programming problems. In this case, optimization algorithms can only be guaranteed to produce an (approximate) local optimum, but all local optima are close in value to the global optimum.

Biography

Andrea Montanari received a Laurea degree in Physics in 1997, and a Ph. D. in Theoretical Physics in 2001 (both from Scuola Normale Superiore in Pisa, Italy). He has been post-doctoral fellow at Laboratoire de Physique Théorique de l'Ecole Normale Supérieure (LPTENS), Paris, France, and the Mathematical Sciences Research Institute, Berkeley, USA. Since 2002 he is Chargé de Recherche (with Centre National de la Recherche Scientifique, CNRS) at LPTENS. In September 2006, he joined Stanford University as a faculty, and since 2015 he is Full Professor in the Departments of Electrical Engineering and Statistics.

He was co-awarded the ACM SIGMETRICS best paper award in 2008. He received the CNRS bronze medal for theoretical physics in 2006, the National Science Foundation CAREER award in 2008, the Okawa Foundation Research Grant in 2013, and the Applied Probability Society Best Publication Award in 2015. He is an Information Theory Society distinguished lecturer for 2015-2016. In 2016, he received the James L. Massey Research & Teaching Award of the Information Theory Society for young scholars.

Reception information

Reception to follow at 5 PM.