# Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty

arXiv: https://arxiv.org/abs/2608.05454 · HTML: https://mlsanity.com/paper/2608.05454/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 30 of 33)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting](https://mlsanity.com/paper/2301.00493/) (2023)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Remember Intentions: Retrospective-Memory-based Trajectory Prediction](https://mlsanity.com/paper/2203.11474/) (2022)
- [SmartRefine: A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction](https://mlsanity.com/paper/2403.11492/) (2024)
- [FloMo: Tractable Motion Prediction with Normalizing Flows](https://mlsanity.com/paper/2103.03614/) (2021)
- [DeMo: Decoupling Motion Forecasting into Directional Intentions and Dynamic States](https://mlsanity.com/paper/2410.05982/) (2024)
- [Motion Forecasting in Continuous Driving](https://mlsanity.com/paper/2410.06007/) (2024)

## Abstract (arXiv)

Probabilistic prediction heads in neural networks typically output either a Gaussian mixture or a single conformal region. Neither separates the distinct sources of uncertainty often present in real prediction tasks: a discrete choice among modes, bounded systematic drift within the chosen mode, and irreducible stochastic noise. We introduce the Hybrid Probabilistic Zonotope (HProbZ), an output head that represents these three sources as binary, bounded, and stochastic generators of a zonotope, and admits a closed-form likelihood by convolution. Sharing the bounded generator across prediction steps couples future predictions algebraically, so observing one step refines the predictive distribution at every remaining step in a single forward pass. We establish that the three generators are identifiable from the likelihood up to permutation, and that an HProbZ density is representationally distinct from any finite Gaussian mixture. The same shared structure provides analytic per-mode risk and distribution-free multi-modal conformal sets at inference time. Empirical analysis on representative prediction benchmarks supports the effectiveness of the design relative to same-encoder mixture baselines, while offering structural properties that mixture or convex-conformal predictors do not jointly provide.