# Distribution Preserving Multiple Hypotheses Prediction for Uncertainty Modeling

arXiv: https://arxiv.org/abs/2110.02858 · HTML: https://mlsanity.com/paper/2110.02858/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [Unsupervised Learning for Physical Interaction through Video Prediction](https://mlsanity.com/paper/1605.07157/) (2016)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Overcoming Limitations of Mixture Density Networks: A Sampling and Fitting Framework for Multimodal Future Prediction](https://mlsanity.com/paper/1906.03631/) (2019)
- [Distributional Clustering: A distribution-preserving clustering method](https://mlsanity.com/paper/1911.05940/) (2019)

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

- [Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction](https://mlsanity.com/paper/2309.00781/) (2023)
- [Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity](https://mlsanity.com/paper/2509.02792/) (2025)

## Abstract (arXiv)

Many supervised machine learning tasks, such as future state prediction in dynamical systems, require precise modeling of a forecast's uncertainty. The Multiple Hypotheses Prediction (MHP) approach addresses this problem by providing several hypotheses that represent possible outcomes. Unfortunately, with the common l2 loss function, these hypotheses do not preserve the data distribution's characteristics. We propose an alternative loss for distribution preserving MHP and review relevant theorems supporting our claims. Furthermore, we empirically show that our approach yields more representative hypotheses on a synthetic and a real-world motion prediction data set. The outputs of the proposed method can directly be used in sampling-based Monte-Carlo methods.