Distribution Preserving Multiple Hypotheses Prediction for Uncertainty Modeling
This work addresses uncertainty modeling for dynamical systems prediction, but it is incremental as it modifies an existing approach to better preserve data distributions.
The paper tackles the problem of uncertainty modeling in supervised machine learning tasks, such as future state prediction, by proposing a distribution preserving loss for Multiple Hypotheses Prediction, which yields more representative hypotheses on synthetic and real-world motion prediction datasets.
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 $l_2$ 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.