Bayesian meta learning for trustworthy uncertainty quantification
This work addresses uncertainty quantification in Bayesian regression for applications requiring reliable probabilistic predictions, though it appears incremental as it builds on existing meta-learning methods.
The paper tackles the problem of Bayesian regression with trustworthy uncertainty quantification, proposing Trust-Bayes, a novel optimization framework for Bayesian meta learning that ensures ground truth is captured by predictive intervals with a pre-specified probability, and verifies it through Monte Carlo simulations showing improved performance over Meta-prior.
We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive distributions with a pre-specified probability. Furthermore, we propose, Trust-Bayes, a novel optimization framework for Bayesian meta learning which is cognizant of trustworthy uncertainty quantification without explicit assumptions on the prior model/distribution of the functions. We characterize the lower bounds of the probabilities of the ground truth being captured by the specified intervals and analyze the sample complexity with respect to the feasible probability for trustworthy uncertainty quantification. Monte Carlo simulation of a case study using Gaussian process regression is conducted for verification and comparison with the Meta-prior algorithm.