Abstract
Quantifying data uncertainties and expressing model uncertainties is a challenging yet crucial task in machine learning. While deep learning has become a dominant tool in modern machine learning applications, most deep learning models do not provide reliable confidence in their predictions. In this thesis, we aim to develop practical tools for deep learning-based uncertainty quantification methods.
To begin with, we pay attention to a fundamental and important problem in uncertainty quantification, namely how to efficiently measure the distance between probability distributions in high-dimensional spaces. We propose a new family of optimal transport (OT) distance metrics that are data-adaptive and efficient in high-dimensional spaces. We then focus on measuring the uncertainties and propagating model uncertainties in sequential data with the recently emerging filtering technique called differentiable particle filters (DPFs). We provide a mechanism to construct and learn expressive components of differentiable particle filters in a flexible way. Moreover, we extend differentiable particle filters to continuous-discrete cases, allowing one to evaluate the model uncertainty at irregularly distributed time stamps. Lastly, we develop a novel uncertainty quantification method to address the out-of-distribution detection problem.