  We develop a Bayesian approach to learning from sequential data by using
Gaussian processes (GPs) with so-called signature kernels as covariance
functions. This allows to make sequences of different length comparable and to
rely on strong theoretical results from stochastic analysis. Signatures capture
sequential structure with tensors that can scale unfavourably in sequence
length and state space dimension. To deal with this, we introduce a sparse
variational approach with inducing tensors. We then combine the resulting GP
with LSTMs and GRUs to build larger models that leverage the strengths of each
of these approaches and benchmark the resulting GPs on multivariate time series
(TS) classification datasets. Code available at
https://github.com/tgcsaba/GPSig.
