Calculus of Variations and Geometric Measure Theory

Mathematical problems in modern machine learning

Andrea Montanari

created by novaga on 09 Apr 2020
modified on 14 Apr 2020

15 apr 2020 -- 16:00   [open in google calendar]

Abstract.

The last fifteen years have witnessed dramatic advances in machine learning. This progress was mainly driven by engineering advances: greater computing power, and larger availability of training data. Not only the collection of methods that emerged from this revolution are not well understood mathematically, but they actually appear to defy traditional mathematical theories of machine learning.

I will argue that future developments and applications will require to understand better the underlying mathematical principles.

I will describe two recent examples of mathematical progress in this area that are connected to areas of modern mathematics:

1. Gradient flows in Wasserstein spaces;

2. Random matrix theory.

Based on joint work with: Song Mei, Phan-Minh Nguyen, Behrooz Ghorbani, Theodor Misiakiewicz.