ICME Weekly Seminar Digest

MONDAY, DECEMBER 5, 2016:
CME 500: Departmental Seminar
Speaker: Song Mei, ICME graduate student

Title: The Landscape of Empirical Risk for Non-convex Losses

Abstract: Most high-dimensional estimation and prediction methods propose to minimize the empirical risk that is written as a sum of losses associated to each data point. In this talk we focus on the case of non-convex losses, that is practically important but still poorly understood. Classical empirical process theory implies uniform convergence of the empirical risk to the population risk. While uniform convergence implies consistency of the resulting M-estimator, it does not ensure that the latter can be computed efficiently. 

Empirical risk minimization is often carried out via first-order algorithms such as gradient descent and its generalizations. In order to capture the complexity of computing M-estimators, we propose to study the landscape of the empirical risk, namely its stationary points and their properties. We establish uniform convergence of the gradient and Hessian of the empirical risk to their population counterparts, as soon as the number of samples becomes larger than the number of unknown parameters (modulo logarithmic factors). We demonstrate that –in several examples– this result implies a complete characterization of the landscape of the empirical risk, and of the convergence properties of descent algorithms.

Location: Y2E2-111
Time: 4:30-5:20 p.m.

TUESDAY, DECEMBER 6, 2016:
CME 300: First Year Seminar Series
Please join us for two speakers this week:

Speaker: Lexing Ying, Professor of Mathematics

Description: My talk titled, "Efficient algorithms for highly oscillatory problems: a sparse approach", will address recent work on computational high frequency wave, computational chemistry, and multi-way clustering.

Speaker: Aaron Sidford, Assistant Professor of Management Science and Engineering

Description: In this talk I will provide an overview of my research in developing provably faster algorithms for solving fundamental and pervasive problems in optimization. Over the past decade there have been numerous breakthroughs in designing efficient algorithms for these problems by leveraging and building upon a broad set of techniques including iterative methods, randomized numerical linear algebra, spectral graph theory, and more. In this talk I will highlight this work by survey recent improvements in solving graph optimization problems known as flow problems, and explain why I believe this is just the beginning.

Location: Y2E2-101
Time: 12:30-1:20 p.m.