  There is a gap in risk assessment of trajectories between the trajectory
information coming from a traffic motion prediction module and what is actually
needed. Closing this gap necessitates advancements in prediction beyond current
practices. Existing prediction models yield joint predictions of agents' future
trajectories with uncertainty weights or marginal Gaussian probability density
functions (PDFs) for single agents. Although, these methods achieve high
accurate trajectory predictions, they only provide little or no information
about the dependencies of interacting agents. Since traffic is a process of
highly interdependent agents, whose actions directly influence their mutual
behavior, the existing methods are not sufficient to reliably assess the risk
of future trajectories. This paper addresses that gap by introducing a novel
approach to motion prediction, focusing on predicting agent-pair covariance
matrices in a ``scene-centric'' manner, which can then be used to model
Gaussian joint PDFs for all agent-pairs in a scene. We propose a model capable
of predicting those agent-pair covariance matrices, leveraging an enhanced
awareness of interactions. Utilizing the prediction results of our model, this
work forms the foundation for comprehensive risk assessment with statistically
based methods for analyzing agents' relations by their joint PDFs.
