Deep hybrid model. Probabilistic graphi-
cal model for weather prediction where weather sta-
tions denoted by S, induce a Gaussian process (GP)
prior over the true values of the weather variables
W. Only noisier versions (zi) of the true values are
observed at all the sites and are related via . The
forecasts given by the pre-trained predictor are re-
lated to the future observations via the potential
(). The joint distribution of the true weather vari-
ables is further constrained via a deep belief network
(()). All potentials arise at a test site s, except
that there is no pre-trained predictor.