  We build a model using Gaussian processes to infer a spatio-temporal vector
field from observed agent trajectories. Significant landmarks or influence
points in agent surroundings are jointly derived through vector calculus
operations that indicate presence of sources and sinks. We evaluate these
influence points by using the Kullback-Leibler divergence between the posterior
and prior Laplacian of the inferred spatio-temporal vector field. Through
locating significant features that influence trajectories, our model aims to
give greater insight into underlying causal utility functions that determine
agent decision-making. A key feature of our model is that it infers a joint
Gaussian process over the observed trajectories, the time-varying vector field
of utility and canonical vector calculus operators. We apply our model to both
synthetic data and lion GPS data collected at the Bubye Valley Conservancy in
southern Zimbabwe.
