  Sparse Gaussian processes and various extensions thereof are enabled through
inducing points, that simultaneously bottleneck the predictive capacity and act
as the main contributor towards model complexity. However, the number of
inducing points is generally not associated with uncertainty which prevents us
from applying the apparatus of Bayesian reasoning for identifying an
appropriate trade-off. In this work we place a point process prior on the
inducing points and approximate the associated posterior through stochastic
variational inference. By letting the prior encourage a moderate number of
inducing points, we enable the model to learn which and how many points to
utilise. We experimentally show that fewer inducing points are preferred by the
model as the points become less informative, and further demonstrate how the
method can be employed in deep Gaussian processes and latent variable
modelling.
