**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Tuesday, November 21, 2023 1:00 PM EST

Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link)

Hrushikesh Mhaskar, Research Professor of Mathematics, Claremont Graduate University, Institute of Mathematical Sciences

Theory of machine learning revisited

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.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.