Epistemic and Aleatoric Uncertainty Quantification for Gaussian Processes

Pau is a PhD student in Computing and Mathematical Sciences at Caltech, advised by Houman Owhadi. His main research area is Game-theoretical Uncertainty Quantification (UQ) and Gaussian Process Regression (GPR), both from a theoretical point of view and with applications to the Physical Sciences, including collaboration with scientists from the Machine Learning and Uncertainty Quantification groups at NASA Jet Propulsion Laboratory. Before joining Caltech, he graduated from Universitat Politècnica de Catalunya with a double degree in Mathematics and Engineering Physics as part of the CFIS program and he was a research intern at the Center for Data Science at NYU for 9 months. One of the major advantages of using Gaussian Processes for regression and surrogate modeling is the availability of uncertainty bounds for the predictions. However, the validity of these bounds depends on using an appropriate covariance function, which is usually learned from the data out of a parametric family through maximum likelihood estimation or cross-validation methods. In practice, the data might not contain enough information to select the best covariance function, generating uncertainty in the hyperparameters, which translates into an additional layer of uncertainty in the predictions (epistemic uncertainty) on top of the usual posterior covariance (aleatoric uncertainty). In this talk, we discuss considering both uncertainties for UQ, and we quantify them by extending the MLE paradigm using a game theoretical framework that identifies the worst-case prior under a likelihood constraint specified by the practitioner.