# Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses

arXiv: https://arxiv.org/abs/1612.00197 · HTML: https://mlsanity.com/paper/1612.00197/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2016.

## Built on by (most cited first, 30 of 97)

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- [Non-Probability Sampling Network for Stochastic Human Trajectory Prediction](https://mlsanity.com/paper/2203.13471/) (2022)
- [Interpretable Social Anchors for Human Trajectory Forecasting in Crowds](https://mlsanity.com/paper/2105.03136/) (2021)
- [EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2307.09306/) (2023)
- [Probabilistic 3D Human Shape and Pose Estimation from Multiple Unconstrained Images in the Wild](https://mlsanity.com/paper/2103.10978/) (2021)
- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [Divide-and-Conquer for Lane-Aware Diverse Trajectory Prediction](https://mlsanity.com/paper/2104.08277/) (2021)
- [Transframer: Arbitrary Frame Prediction with Generative Models](https://mlsanity.com/paper/2203.09494/) (2022)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Uncertainty Estimation via Response Scaling for Pseudo-mask Noise Mitigation in Weakly-supervised Semantic Segmentation](https://mlsanity.com/paper/2112.07431/) (2021)
- [Stochastic Multi-Person 3D Motion Forecasting](https://mlsanity.com/paper/2306.05421/) (2023)
- [HuManiFlow: Ancestor-Conditioned Normalising Flows on SO(3) Manifolds for Human Pose and Shape Distribution Estimation](https://mlsanity.com/paper/2305.06968/) (2023)
- [Bootstrap Motion Forecasting With Self-Consistent Constraints](https://mlsanity.com/paper/2204.05859/) (2022)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Injecting Knowledge in Data-driven Vehicle Trajectory Predictors](https://mlsanity.com/paper/2103.04854/) (2021)
- [Using Soft Labels to Model Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/2109.12622/) (2021)
- [Modeling Multimodal Aleatoric Uncertainty in Segmentation with Mixture of Stochastic Experts](https://mlsanity.com/paper/2212.07328/) (2022)
- [That Label's Got Style: Handling Label Style Bias for Uncertain Image Segmentation](https://mlsanity.com/paper/2303.15850/) (2023)
- [Uncertainty-aware Medical Diagnostic Phrase Identification and Grounding](https://mlsanity.com/paper/2404.06798/) (2024)
- [Diverse Multiple Trajectory Prediction Using a Two-stage Prediction Network Trained with Lane Loss](https://mlsanity.com/paper/2206.08641/) (2022)
- [Safety-compliant Generative Adversarial Networks for Human Trajectory Forecasting](https://mlsanity.com/paper/2209.12243/) (2022)
- [Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysis](https://mlsanity.com/paper/2311.01052/) (2023)
- [Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealing](https://mlsanity.com/paper/2407.15580/) (2024)
- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2303.13123/) (2023)
- [Moving SLAM: Fully Unsupervised Deep Learning in Non-Rigid Scenes](https://mlsanity.com/paper/2105.02195/) (2021)
- [CT Image Synthesis Using Weakly Supervised Segmentation and Geometric Inter-Label Relations For COVID Image Analysis](https://mlsanity.com/paper/2106.10230/) (2021)

## Abstract (arXiv)

Many prediction tasks contain uncertainty. In some cases, uncertainty is inherent in the task itself. In future prediction, for example, many distinct outcomes are equally valid. In other cases, uncertainty arises from the way data is labeled. For example, in object detection, many objects of interest often go unlabeled, and in human pose estimation, occluded joints are often labeled with ambiguous values. In this work we focus on a principled approach for handling such scenarios. In particular, we propose a framework for reformulating existing single-prediction models as multiple hypothesis prediction (MHP) models and an associated meta loss and optimization procedure to train them. To demonstrate our approach, we consider four diverse applications: human pose estimation, future prediction, image classification and segmentation. We find that MHP models outperform their single-hypothesis counterparts in all cases, and that MHP models simultaneously expose valuable insights into the variability of predictions.