Bayesian meta learning for trustworthy uncertainty quantification

TL;DR

This paper introduces Trust-Bayes, a Bayesian meta learning framework that ensures trustworthy uncertainty quantification in regression tasks, verified through Gaussian process simulations.

Contribution

It proposes a novel optimization framework for Bayesian meta learning focused on trustworthy uncertainty quantification without relying on explicit prior assumptions.

Findings

Characterizes lower bounds for probability of ground truth within predictive intervals

Analyzes sample complexity for achieving trustworthy uncertainty quantification

Verifies approach through Gaussian process regression simulations

Abstract

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.