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