# Uncertainty-Aware Learning from Demonstration using Mixture Density Networks with Sampling-Free Variance Modeling

arXiv: https://arxiv.org/abs/1709.02249 · HTML: https://mlsanity.com/paper/1709.02249/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2017.

## Built on by (most cited first, 25 of 25)

- [Active Learning for Deep Object Detection via Probabilistic Modeling](https://mlsanity.com/paper/2103.16130/) (2021)
- [A Survey of Deep RL and IL for Autonomous Driving Policy Learning](https://mlsanity.com/paper/2101.01993/) (2021)
- [Unbiased Scene Graph Generation in Videos](https://mlsanity.com/paper/2304.00733/) (2023)
- [Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives](https://mlsanity.com/paper/1903.02114/) (2019)
- [Learning Uncertainty For Safety-Oriented Semantic Segmentation In Autonomous Driving](https://mlsanity.com/paper/2105.13688/) (2021)
- [Beyond Confidence: Adaptive Abstention in Dual-Threshold Conformal Prediction for Autonomous System Perception](https://mlsanity.com/paper/2502.07255/) (2025)
- [Learn by Observation: Imitation Learning for Drone Patrolling from Videos of A Human Navigator](https://mlsanity.com/paper/2008.13193/) (2020)
- [SOTIF Entropy: Online SOTIF Risk Quantification and Mitigation for Autonomous Driving](https://mlsanity.com/paper/2211.04009/) (2022)
- [Enhancing Uncertainty Quantification in Drug Discovery with Censored Regression Labels](https://mlsanity.com/paper/2409.04313/) (2024)
- [Uncertainty-Aware Autonomous Vehicles: Predicting the Road Ahead](https://mlsanity.com/paper/2510.22680/) (2025)
- [Adversarial Mixture Density Networks: Learning to Drive Safely from Collision Data](https://mlsanity.com/paper/2107.04485/) (2021)
- [Learning to Predict Diverse Human Motions from a Single Image via Mixture Density Networks](https://mlsanity.com/paper/2109.05776/) (2021)
- [Estimating Uncertainty For Vehicle Motion Prediction on Yandex Shifts Dataset](https://mlsanity.com/paper/2112.08355/) (2021)
- [Towards Defensive Autonomous Driving: Collecting and Probing Driving Demonstrations of Mixed Qualities](https://mlsanity.com/paper/2109.07995/) (2021)
- [Anticipatory Planning: Improving Long-Lived Planning by Estimating Expected Cost of Future Tasks](https://mlsanity.com/paper/2305.04692/) (2023)
- [Sampling-based Uncertainty Estimation for an Instance Segmentation Network](https://mlsanity.com/paper/2305.14977/) (2023)
- [Semi-Supervised Imitation Learning with Mixed Qualities of Demonstrations for Autonomous Driving](https://mlsanity.com/paper/2109.11280/) (2021)
- [Uncertainty Estimation in Deep Speech Enhancement Using Complex Gaussian Mixture Models](https://mlsanity.com/paper/2212.04831/) (2022)
- [Robust Calibration For Improved Weather Prediction Under Distributional Shift](https://mlsanity.com/paper/2401.04144/) (2024)
- [Double-Shot 3D Shape Measurement with a Dual-Branch Network for Structured Light Projection Profilometry](https://mlsanity.com/paper/2407.14198/) (2024)
- [Off the Normal Path: Learning Spatial Density Models of Node Mobility](https://mlsanity.com/paper/2411.10997/) (2024)
- [TSceneJAL: Joint Active Learning of Traffic Scenes for 3D Object Detection](https://mlsanity.com/paper/2412.18870/) (2024)
- [Adaptive Individual Uncertainty under Out-Of-Distribution Shift with Expert-Routed Conformal Prediction](https://mlsanity.com/paper/2510.15233/) (2025)
- [Where to Measure: Epistemic Uncertainty-Based Sensor Placement with ConvCNPs](https://mlsanity.com/paper/2511.22567/) (2025)
- [Taming Perception Jitter: Uncertainty-Aware LiDAR Object Detection for Reliable Motion Classification](https://mlsanity.com/paper/2606.09350/) (2026)

## Abstract (arXiv)

In this paper, we propose an uncertainty-aware learning from demonstration method by presenting a novel uncertainty estimation method utilizing a mixture density network appropriate for modeling complex and noisy human behaviors. The proposed uncertainty acquisition can be done with a single forward path without Monte Carlo sampling and is suitable for real-time robotics applications. The properties of the proposed uncertainty measure are analyzed through three different synthetic examples, absence of data, heavy measurement noise, and composition of functions scenarios. We show that each case can be distinguished using the proposed uncertainty measure and presented an uncertainty-aware learn- ing from demonstration method of an autonomous driving using this property. The proposed uncertainty-aware learning from demonstration method outperforms other compared methods in terms of safety using a complex real-world driving dataset.