# Reliable Multimodal Trajectory Prediction via Error Aligned Uncertainty Optimization

arXiv: https://arxiv.org/abs/2212.04812 · HTML: https://mlsanity.com/paper/2212.04812/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 9 Dec 2022.

## Builds on (most cited first, 27 of 27)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representation](https://mlsanity.com/paper/2005.04259/) (2020)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [Multimodal Motion Prediction with Stacked Transformers](https://mlsanity.com/paper/2103.11624/) (2021)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Can Autonomous Vehicles Identify, Recover From, and Adapt to Distribution Shifts?](https://mlsanity.com/paper/2006.14911/) (2020)
- [Improving model calibration with accuracy versus uncertainty optimization](https://mlsanity.com/paper/2012.07923/) (2020)
- [Rules of the Road: Predicting Driving Behavior with a Convolutional Model of Semantic Interactions](https://mlsanity.com/paper/1906.08945/) (2019)
- [Implicit Latent Variable Model for Scene-Consistent Motion Forecasting](https://mlsanity.com/paper/2007.12036/) (2020)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Deep Imitative Models for Flexible Inference, Planning, and Control](https://mlsanity.com/paper/1810.06544/) (2018)
- [Depth Uncertainty in Neural Networks](https://mlsanity.com/paper/2006.08437/) (2020)
- [Uncertainty-Aware Driver Trajectory Prediction at Urban Intersections](https://mlsanity.com/paper/1901.05105/) (2019)
- [Improving Uncertainty Calibration of Deep Neural Networks via Truth Discovery and Geometric Optimization](https://mlsanity.com/paper/2106.14662/) (2021)

## Built on by (most cited first, 2 of 2)

- [BEA: Revisiting anchor-based object detection DNN using Budding Ensemble Architecture](https://mlsanity.com/paper/2309.08036/) (2023)
- [Is It Certainly a Deepfake? Reliability Analysis in Detection & Generation Ecosystem](https://mlsanity.com/paper/2509.17550/) (2025)

## Abstract (arXiv)

Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is challenging as ground truth for uncertainty estimates is not available. Ideally, in a well-calibrated model, uncertainty estimates should perfectly correlate with model error. We propose a novel error aligned uncertainty optimization method and introduce a trainable loss function to guide the models to yield good quality uncertainty estimates aligning with the model error. Our approach targets continuous structured prediction and regression tasks, and is evaluated on multiple datasets including a large-scale vehicle motion prediction task involving real-world distributional shifts. We demonstrate that our method improves average displacement error by 1.69% and 4.69%, and the uncertainty correlation with model error by 17.22% and 19.13% as quantified by Pearson correlation coefficient on two state-of-the-art baselines.