When: Apr 28 2022 @ 1:30 PM

Title: Beyond Regression: Operators and Extrapolation in Machine Learning

Abstract: In this talk we first suggest a unification of regression-based machine learning methods, including kernel regression and various types of neural networks.  We then consider the limitations of such methods, especially the curse-of-dimensionality, and the various potential solutions that have been proposed including: (1) Barron’s existence result, (2) leveraging regularity, and (3) assuming special structure in the data such as independence or redundancy.  Finally, we consider operator-learning and extrapolation as emerging directions for machine learning.  Operator-learning is the more developed of the two, and we show how learning operators allows intrinsic regularization, uncertainty quantification, and can represent many-to-one and one-to-many mappings.  However, extrapolation remains the final frontier in machine learning, and we discuss an emerging approach and the mathematics that may underly it.  

Here is the zoom link is:  https://wse.zoom.us/j/95448608570