  This paper presents a data-driven approach to model planar pushing
interaction to predict both the most likely outcome of a push and its expected
variability. The learned models rely on a variation of Gaussian processes with
input-dependent noise called Variational Heteroscedastic Gaussian processes
(VHGP) that capture the mean and variance of a stochastic function. We show
that we can learn accurate models that outperform analytical models after less
than 100 samples and saturate in performance with less than 1000 samples. We
validate the results against a collected dataset of repeated trajectories, and
use the learned models to study questions such as the nature of the variability
in pushing, and the validity of the quasi-static assumption.
