# Spatial Uncertainty Sampling for End-to-End Control

arXiv: https://arxiv.org/abs/1805.04829 · HTML: https://mlsanity.com/paper/1805.04829/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2018.

## Built on by (most cited first, 13 of 13)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [VRA: Variational Rectified Activation for Out-of-distribution Detection](https://mlsanity.com/paper/2302.11716/) (2023)
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- [Symmetrical SyncMap for Imbalanced General Chunking Problems](https://mlsanity.com/paper/2310.10045/) (2023)
- [Marginally calibrated response distributions for end-to-end learning in autonomous driving](https://mlsanity.com/paper/2110.01050/) (2021)
- [Frequency Dropout: Feature-Level Regularization via Randomized Filtering](https://mlsanity.com/paper/2209.09844/) (2022)
- [Evidence-based Match-status-Aware Gait Recognition for Out-of-Gallery Gait Identification](https://mlsanity.com/paper/2211.08007/) (2022)
- [I-GLIDE: Input Groups for Latent Health Indicators in Degradation Estimation](https://mlsanity.com/paper/2511.21208/) (2025)
- [Evaluating deep learning models for fault diagnosis of a rotating machinery with epistemic and aleatoric uncertainty](https://mlsanity.com/paper/2412.18980/) (2024)
- [Enhancing Out-of-Distribution Detection with Multitesting-based Layer-wise Feature Fusion](https://mlsanity.com/paper/2403.10803/) (2024)
- [Customer Lifetime Value Prediction with Uncertainty Estimation Using Monte Carlo Dropout](https://mlsanity.com/paper/2411.15944/) (2024)
- [Single-Eye View: Monocular Real-time Perception Package for Autonomous Driving](https://mlsanity.com/paper/2603.21061/) (2026)
- [A Cubing Strategy for Identifying Stable Hyperparameter Regions for Uncertainty Quantification in Spatial Deep Learning](https://mlsanity.com/paper/2605.16570/) (2026)

## Abstract (arXiv)

End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions, ambiguous navigation situations, and safety considerations require reliable uncertainty estimation for the eventual adoption of full-scale autonomous vehicles. Bayesian deep learning approaches provide a way to estimate uncertainty by approximating the posterior distribution of weights given a set of training data. Dropout training in deep NNs approximates Bayesian inference in a deep Gaussian process and can thus be used to estimate model uncertainty. In this paper, we propose a Bayesian NN for end-to-end control that estimates uncertainty by exploiting feature map correlation during training. This approach achieves improved model fits, as well as tighter uncertainty estimates, than traditional element-wise dropout. We evaluate our algorithms on a challenging dataset collected over many different road types, times of day, and weather conditions, and demonstrate how uncertainties can be used in conjunction with a human controller in a parallel autonomous setting.