  Trajectory prediction in a cluttered environment is key to many important
robotics tasks such as autonomous navigation. However, there are an infinite
number of possible trajectories to consider. To simplify the space of
trajectories under consideration, we utilise homotopy classes to partition the
space into countably many mathematically equivalent classes. All members within
a class demonstrate identical high-level motion with respect to the
environment, i.e., travelling above or below an obstacle. This allows
high-level prediction of a trajectory in terms of a sparse label identifying
its homotopy class. We therefore present a light-weight learning framework
based on variable-order Markov processes to learn and predict homotopy classes
and thus high-level agent motion. By informing a Gaussian Mixture Model (GMM)
with our homotopy class predictions, we see great improvements in low-level
trajectory prediction compared to a naive GMM on a real dataset.
