Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link)
Speaker
Hrushikesh Mhaskar, Research Professor of Mathematics, Claremont Graduate University, Institute of Mathematical Sciences
Title
Theory of machine learning revisited
Abstract
Although the fundamental problem of machine learning is often posed as one of function approximation, classical approximation theory has played only a marginal role in machine learning. We present new tools which enable us in theory to solve the problem of estimating a function on an unknown manifold based on noisy data. In contrast to existing solutions to this problem, which require first finding some further quantities related to the manifold, such as an atlas or eigen-decomposition of the Laplace-Beltrami operator, our method is a simple one shot approach, and provided guaranteed rates of approximation. We argue that the problem of classification can be viewed as the problem of separating the supports of the probability distributions corresponding to various classes. The problem of super-resolution is a special case, where the distributions are point masses. The tools which we have developed for the problem of function approximation can be used in a dual manner to solve this problem.