Princeton University

School of Engineering & Applied Science

Geometry in large scale statistical learning & optimization problems

Feng Ruan, Stanford University
B205 Engineering Quadrangle
Tuesday, March 19, 2019 - 4:30pm


Geometric ideas have been crucial to the understanding of fundamental limits and development of optimal algorithms in statistical learning, optimization, and signal processing. Classical examples include the Fisher information (and related information geometry concepts) and maximum likelihood estimators in statistics and condition numbers in numerical optimization and inverse problems. In this talk, I will bring these geometric ideas into contact with modern large-scale learning and optimization problems, focusing specifically on problems in privacy-preserving data analysis, stochastic convex optimization, and composite optimization (a class of optimization problems beyond convexity). For private learning and stochastic convex optimization problems, I will derive new analogues of the Fisher information that precisely characterize tradeoffs between statistical efficiency, privacy, and computation, enabling the development of new optimal statistical and optimization procedures (analogues of maximum likelihood estimators). Similarly, for composite optimization, these geometric ideas facilitate the design of objectives with both better fidelity to underlying scientific problems-including phase retrieval-and benign optimization landscapes, allowing the development of efficient and information-theoretically optimal optimization methods.


Feng Ruan is a fifth year Ph.D. student in the Department of Statistics at Stanford University, advised by Prof. John Duchi. He is broadly interested in developing theory and algorithm for inference under resource constraints, for stochastic convex and nonconvex optimization, and for high dimensional statistics. He is a recipient of the E.K. Potter Stanford Graduate Fellowship from Stanford University.