  We present a computationally-efficient strategy to initialise the
hyperparameters of a Gaussian process (GP) avoiding the computation of the
likelihood function. Our strategy can be used as a pretraining stage to find
initial conditions for maximum-likelihood (ML) training, or as a standalone
method to compute hyperparameters values to be plugged in directly into the GP
model. Motivated by the fact that training a GP via ML is equivalent (on
average) to minimising the KL-divergence between the true and learnt model, we
set to explore different metrics/divergences among GPs that are computationally
inexpensive and provide hyperparameter values that are close to those found via
ML. In practice, we identify the GP hyperparameters by projecting the empirical
covariance or (Fourier) power spectrum onto a parametric family, thus proposing
and studying various measures of discrepancy operating on the temporal and
frequency domains. Our contribution extends the variogram method developed by
the geostatistics literature and, accordingly, it is referred to as the
generalised variogram method (GVM). In addition to the theoretical presentation
of GVM, we provide experimental validation in terms of accuracy, consistency
with ML and computational complexity for different kernels using synthetic and
real-world data.
