Identifying Sources and Sinks in the Presence of Multiple Agents with Gaussian Process Vector Calculus

TL;DR

GP-LAPLACE is a novel Gaussian process-based method that identifies sources and sinks in dynamic multi-agent systems solely from trajectory data, without prior environment knowledge, and quantifies the significance of inferred features.

Contribution

This work introduces GP-LAPLACE, a probabilistic approach that jointly infers spatio-temporal vector fields and their derivatives from agent trajectories, overcoming limitations of environment-dependent models.

Findings

Successfully applied to synthetic and real GPS data.

Demonstrates superiority over existing methods.

Effectively identifies influential sources and sinks.

Abstract

In systems of multiple agents, identifying the cause of observed agent dynamics is challenging. Often, these agents operate in diverse, non-stationary environments, where models rely on hand-crafted environment-specific features to infer influential regions in the system's surroundings. To overcome the limitations of these inflexible models, we present GP-LAPLACE, a technique for locating sources and sinks from trajectories in time-varying fields. Using Gaussian processes, we jointly infer a spatio-temporal vector field, as well as canonical vector calculus operations on that field. Notably, we do this from only agent trajectories without requiring knowledge of the environment, and also obtain a metric for denoting the significance of inferred causal features in the environment by exploiting our probabilistic method. To evaluate our approach, we apply it to both synthetic and real-world GPS data, demonstrating the applicability of our technique in the presence of multiple agents, as well as its superiority over existing methods.