# Bayesian meta learning for trustworthy uncertainty quantification

arXiv: https://arxiv.org/abs/2407.19287 · HTML: https://mlsanity.com/paper/2407.19287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 27 Jul 2024.

## Builds on (most cited first, 20 of 20)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Shallow Bayesian Meta Learning for Real-World Few-Shot Recognition](https://mlsanity.com/paper/2101.02833/) (2021)
- [Meta-Learning Sparse Implicit Neural Representations](https://mlsanity.com/paper/2110.14678/) (2021)
- [Generalization of Model-Agnostic Meta-Learning Algorithms: Recurring and Unseen Tasks](https://mlsanity.com/paper/2102.03832/) (2021)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics](https://mlsanity.com/paper/1712.09983/) (2017)
- [Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework](https://mlsanity.com/paper/2008.11700/) (2020)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [Bayesian Meta-Prior Learning Using Empirical Bayes](https://mlsanity.com/paper/2002.01129/) (2020)
- [Lightweight Distributed Gaussian Process Regression for Online Machine Learning](https://mlsanity.com/paper/2105.04738/) (2021)
- [Distributed Safe Learning and Planning for Multi-robot Systems](https://mlsanity.com/paper/2207.07824/) (2022)

## Abstract (arXiv)

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.