  Gaussian processes (GPs) are typically criticised for their unfavourable
scaling in both computational and memory requirements. For large datasets,
sparse GPs reduce these demands by conditioning on a small set of inducing
variables designed to summarise the data. In practice however, for large
datasets requiring many inducing variables, such as low-lengthscale spatial
data, even sparse GPs can become computationally expensive, limited by the
number of inducing variables one can use. In this work, we propose a new class
of inter-domain variational GP, constructed by projecting a GP onto a set of
compactly supported B-spline basis functions. The key benefit of our approach
is that the compact support of the B-spline basis functions admits the use of
sparse linear algebra to significantly speed up matrix operations and
drastically reduce the memory footprint. This allows us to very efficiently
model fast-varying spatial phenomena with tens of thousands of inducing
variables, where previous approaches failed.
