Hrushikesh N. Mhaskar will be guest of the Artificial Intelligence and Mathematics 2022 seminar cycle.

Hrushikesh N. Mhaskar is a research Professor in mathematics at Claremont Graduate University where he deals with approximation theory and harmonic analysis.

The title of the talk is: Machine learning and super-resolution: a unified approach

Abstract of the talk:

Although the fundamental problem of machine learning is often posed as one of function approximation, classicalapproximation theory has played only a marginal role in machine learning.We present new tools which enable us intheory to solve the problem of estimating a function on an unknown manifoldbased on noisy data. In contrast toexisting solutions to this problem, which require first finding somefurther quantities related to the manifold, suchas an atlas or eigen-decomposition of the Laplace-Beltrami operator, ourmethod is a simple one shot approach,and provides guaranteed rates of approximation.We argue that the problem of classification can be viewed as the problem ofseparating the supports of theprobability distributions corresponding to various classes. The problem ofsuper-resolution is a special case, where the distributions are pointmasses.The tools which we have developed for the problem of function approximation can be used in a dual manner to solve this problem.We will present some applications of the theory.