Abstract
We introduce a new interpretation of sparse variational approximations for
Gaussian processes using inducing points which can lead to more scalable
algorithms than previous methods. It is based on decomposing a Gaussian process
as a sum of two independent processes: one in the subspace spanned by the
inducing basis and the other in the orthogonal complement to this subspace. We
show that this formulation recovers existing approximations and at the same
time allows to obtain tighter lower bounds on the marginal likelihood and new
stochastic variational inference algorithms. We demonstrate the efficiency of
these algorithms in several Gaussian process models ranging from standard
regression to multi-class classification using (deep) convolutional Gaussian
processes and report state-of-the-art results on CIFAR-10 with purely GP-based
models.
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