# Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control

arXiv: https://arxiv.org/abs/1909.09884 · HTML: https://mlsanity.com/paper/1909.09884/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2019.

## Built on by (most cited first, 30 of 61)

- [Efficient Deep Reinforcement Learning with Imitative Expert Priors for Autonomous Driving](https://mlsanity.com/paper/2103.10690/) (2021)
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- [Mind the Gap! A Study on the Transferability of Virtual vs Physical-world Testing of Autonomous Driving Systems](https://mlsanity.com/paper/2112.11255/) (2021)
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- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Make Sure You're Unsure: A Framework for Verifying Probabilistic Specifications](https://mlsanity.com/paper/2102.09479/) (2021)
- [Hyperbolic Active Learning for Semantic Segmentation under Domain Shift](https://mlsanity.com/paper/2306.11180/) (2023)
- [Learning Sample Difficulty from Pre-trained Models for Reliable Prediction](https://mlsanity.com/paper/2304.10127/) (2023)
- [UncAD: Towards Safe End-to-end Autonomous Driving via Online Map Uncertainty](https://mlsanity.com/paper/2504.12826/) (2025)
- [Infinite Time Horizon Safety of Bayesian Neural Networks](https://mlsanity.com/paper/2111.03165/) (2021)
- [The Vulnerability of Semantic Segmentation Networks to Adversarial Attacks in Autonomous Driving: Enhancing Extensive Environment Sensing](https://mlsanity.com/paper/2101.03924/) (2021)
- [On the Robustness of Bayesian Neural Networks to Adversarial Attacks](https://mlsanity.com/paper/2207.06154/) (2022)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Predicting Safety Misbehaviours in Autonomous Driving Systems using Uncertainty Quantification](https://mlsanity.com/paper/2404.18573/) (2024)
- [Statistical Perspectives on Reliability of Artificial Intelligence Systems](https://mlsanity.com/paper/2111.05391/) (2021)
- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [SMARLA: A Safety Monitoring Approach for Deep Reinforcement Learning Agents](https://mlsanity.com/paper/2308.02594/) (2023)
- [Explaining Predictive Uncertainty by Exposing Second-Order Effects](https://mlsanity.com/paper/2401.17441/) (2024)
- [Certification of Iterative Predictions in Bayesian Neural Networks](https://mlsanity.com/paper/2105.10134/) (2021)
- [Clarifying Trust of Materials Property Predictions using Neural Networks with Distribution-Specific Uncertainty Quantification](https://mlsanity.com/paper/2302.02595/) (2023)
- [How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2308.12252/) (2023)
- [Adversarial Robustness Certification for Bayesian Neural Networks](https://mlsanity.com/paper/2306.13614/) (2023)
- [Safety Implications of Explainable Artificial Intelligence in End-to-End Autonomous Driving](https://mlsanity.com/paper/2403.12176/) (2024)
- [Reliability Analysis of Artificial Intelligence Systems Using Recurrent Events Data from Autonomous Vehicles](https://mlsanity.com/paper/2102.01740/) (2021)
- [When to Trust AI: Advances and Challenges for Certification of Neural Networks](https://mlsanity.com/paper/2309.11196/) (2023)
- [Discrete-Event Controller Synthesis for Autonomous Systems with Deep-Learning Perception Components](https://mlsanity.com/paper/2202.03360/) (2022)
- [Variational Inference of overparameterized Bayesian Neural Networks: a theoretical and empirical study](https://mlsanity.com/paper/2207.03859/) (2022)
- [Probabilistic Reach-Avoid for Bayesian Neural Networks](https://mlsanity.com/paper/2310.01951/) (2023)
- [Streamlining Prediction in Bayesian Deep Learning](https://mlsanity.com/paper/2411.18425/) (2024)

## Abstract (arXiv)

Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the controller behaviour that properly take account of the uncertainty within the model as well as sensor noise. Bayesian neural networks, which assume a prior over the weights, have been shown capable of producing such uncertainty measures, but properties surrounding their safety have not yet been quantified for use in autonomous driving scenarios. In this paper, we develop a framework based on a state-of-the-art simulator for evaluating end-to-end Bayesian controllers. In addition to computing pointwise uncertainty measures that can be computed in real time and with statistical guarantees, we also provide a method for estimating the probability that, given a scenario, the controller keeps the car safe within a finite horizon. We experimentally evaluate the quality of uncertainty computation by several Bayesian inference methods in different scenarios and show how the uncertainty measures can be combined and calibrated for use in collision avoidance. Our results suggest that uncertainty estimates can greatly aid decision making in autonomous driving.