# On Learning the Tail Quantiles of Driving Behavior Distributions via Quantile Regression and Flows

arXiv: https://arxiv.org/abs/2305.13106 · HTML: https://mlsanity.com/paper/2305.13106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 17 of 17)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [Human Motion Trajectory Prediction: A Survey](https://mlsanity.com/paper/1905.06113/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [TrafficSim: Learning to Simulate Realistic Multi-Agent Behaviors](https://mlsanity.com/paper/2101.06557/) (2021)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Symphony: Learning Realistic and Diverse Agents for Autonomous Driving Simulation](https://mlsanity.com/paper/2205.03195/) (2022)
- [Modeling Human Driving Behavior through Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2006.06412/) (2020)
- [Improving Exploration in Soft-Actor-Critic with Normalizing Flows Policies](https://mlsanity.com/paper/1906.02771/) (2019)
- [Solving inverse problems using conditional invertible neural networks](https://mlsanity.com/paper/2007.15849/) (2020)
- [Forecasting Trajectory and Behavior of Road-Agents Using Spectral Clustering in Graph-LSTMs](https://mlsanity.com/paper/1912.01118/) (2019)
- [Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings](https://mlsanity.com/paper/1503.08195/) (2015)
- [Autoregressive Quantile Flows for Predictive Uncertainty Estimation](https://mlsanity.com/paper/2112.04643/) (2021)
- [Fail-Safe Adversarial Generative Imitation Learning](https://mlsanity.com/paper/2203.01696/) (2022)

## Built on by (most cited first, 1 of 1)

- [Simulating the Unseen: Crash Prediction Must Learn from What Did Not Happen](https://mlsanity.com/paper/2505.21743/) (2025)

## Abstract (arXiv)

Towards safe autonomous driving (AD), we consider the problem of learning models that accurately capture the diversity and tail quantiles of human driver behavior probability distributions, in interaction with an AD vehicle. Such models, which predict drivers' continuous actions from their states, are particularly relevant for closing the gap between AD agent simulations and reality. To this end, we adapt two flexible quantile learning frameworks for this setting that avoid strong distributional assumptions: (1) quantile regression (based on the titled absolute loss), and (2) autoregressive quantile flows (a version of normalizing flows). Training happens in a behavior cloning-fashion. We use the highD dataset consisting of driver trajectories on several highways. We evaluate our approach in a one-step acceleration prediction task, and in multi-step driver simulation rollouts. We report quantitative results using the tilted absolute loss as metric, give qualitative examples showing that realistic extremal behavior can be learned, and discuss the main insights.