Analyzing the Variety Loss in the Context of Probabilistic Trajectory Prediction
This addresses a critical flaw in trajectory prediction for autonomous driving, though it is an incremental improvement focused on loss function correction.
The paper shows that the Minimum over N (MoN) loss used for diversity in probabilistic trajectory prediction does not approximate the true probability density function but its square root, and proposes solutions to correct this, improving log likelihood in experiments.
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.