MS Teams (please email amgrad@uwaterloo.ca for the meeting link)

## Candidate

Yirun Fu | Applied Math, University of Waterloo

## Title

Uniform Error Estimates for Gaussian Processes and Kernel Methods

## Abstract

Gaussian processes and kernel methods are two learning-based approaches to model unknown functions. A major advantage of GPs is the existence of simple analytic formulas for the mean and covariance of the posterior distribution, which allows easy implementations of the algorithms. The models provided by kernel methods also have the same advantage. In order to deploy such learning-based models in safety-critical applications, it is important to rigorously quantify the errors between the learned models and the real physical systems. As a result, we are more interested in obtaining uniform error bounds that the unknown function cannot go beyond or stays in with high probability than an estimation function only. Compared with other existing interval estimations, for example the well-known 95% confidence interval estimation, decisions made under uniform error estimates are significantly safer. In this talk, we will discuss several different error estimates obtained for GPs and kernel methods. We will examine the issues in their assumptions and discuss convergence of the error bounds. We will also show some implementations of these error estimates and evaluate their performance using simple numerical examples.