Department of Applied Mathematics and Statistics
Johns Hopkins University
"Discrete Geometry Meets Machine Learning "
There has been a surge of research activity in machine learning in the past decade. Consequently, there has been a growing interest in mathematically rigorous analysis to strengthen the foundations of this area. A surprisingly large number of applications seem to report empirically observed phenomena that suggest that there are some universal mathematical theorems underpinning the recent successes reported. However, for many of the interesting phenomena, such theoretical foundations have been elusive. Moreover, wherever such results have been obtained, it has been through the lens of continuous (convex and non-convex) optimization. We will try to make the case that techniques from discrete geometry and optimization are ideally placed to tackle some of the unsolved puzzles in this area, and perhaps provide competing methods even in some applications that have traditionally relied on continuous optimization techniques. The emphasis of the talk will be on open problems in machine learning that can be framed in the language of discrete geometry and optimization.