Representing Spatial Trajectories as Distributions

We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts of the trajectory. Our framework allows us to obtain samples from a trajectory for any continuous point in time-both interpolating and extrapolating. Our flexible approach supports directly modifying specific attributes of a trajectory, such as its pace, as well as combining different partial observations into single representations. Experiments show our method's advantage over baselines in prediction tasks. See trajectories.cs.columbia.edu for video results and code.