Distribution Preserving Multiple Hypotheses Prediction for Uncertainty Modeling

TL;DR

This paper introduces a new loss function for Multiple Hypotheses Prediction that better preserves the data distribution, leading to more representative uncertainty modeling in supervised learning tasks.

Contribution

It proposes a distribution-preserving loss for MHP and provides theoretical support and empirical validation on synthetic and real-world motion prediction datasets.

Findings

More representative hypotheses in synthetic data

Improved uncertainty modeling in real-world data

Compatible with sampling-based Monte-Carlo methods

Abstract

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.