PhD Comprehensive Exam | Yirun Fu, Error Bounds Estimate for Gaussian Processes and Kernel Methods and Application in Stability Analysis

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

Candidate

Yirun Fu | Applied Mathematics, University of Waterloo

Title

Error Bounds Estimate for Gaussian Processes and Kernel Methods and Application in Stability Analysis

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. In previous research, an unacceptable assumption has been made and there are deficiencies which result in loss of theoretical guarantees in the experiments. We adjust the assumptions to get more reasonable results and provide numerical examples which is consistent with theoretical results.