Splines and Machine Learning

This lecture by the instructor covers the concept of supervised learning as an ill-posed problem and how constraints are imposed on the solution through regularization. The talk introduces a new representer theorem that characterizes the solution of functional optimization problems, leading to classical algorithms like kernel-based techniques and smoothing splines. The lecture explores the integration of sparse adaptive splines into neural architectures, resulting in high-dimensional adaptive linear splines and deep neural networks with ReLU activations.