# Analyzing the Variety Loss in the Context of Probabilistic Trajectory Prediction

## TL;DR

This paper investigates the variety loss in probabilistic trajectory prediction, revealing it approximates the square root of the true distribution and proposing methods to correct this for better likelihood estimation.

## Contribution

The paper provides a theoretical proof that the variety loss approximates the square root of the true distribution and offers solutions to correct this bias for improved model performance.

## Key findings

- Variety loss approximates the square root of the ground truth distribution.
- Proposed correction methods improve the likelihood estimation.
- Experimental validation on simulated and real datasets supports the theoretical insights.

## Abstract

Trajectory or behavior prediction of traffic agents is an important component of autonomous driving and robot planning in general. It can be framed as a probabilistic future sequence generation problem and recent literature has studied the applicability of generative models in this context. The variety or Minimum over N (MoN) loss, which tries to minimize the error between the ground truth and the closest of N output predictions, has been used in these recent learning models to improve the diversity of predictions. In this work, we present a proof to show that the MoN loss does not lead to the ground truth probability density function, but approximately to its square root instead. We validate this finding with extensive experiments on both simulated toy as well as real world datasets. We also propose multiple solutions to compensate for the dilation to show improvement of log likelihood of the ground truth samples in the corrected probability density function.