  Stochastic Gumbel graph networks are proposed to learn high-dimensional time
series, where the observed dimensions are often spatially correlated. To that
end, the observed randomness and spatial-correlations are captured by learning
the drift and diffusion terms of the stochastic differential equation with a
Gumble matrix embedding, respectively. In particular, this novel framework
enables us to investigate the implicit regularization effect of the noise terms
in S-GGNs. We provide a theoretical guarantee for the proposed S-GGNs by
deriving the difference between the two corresponding loss functions in a small
neighborhood of weight. Then, we employ Kuramoto's model to generate data for
comparing the spectral density from the Hessian Matrix of the two loss
functions. Experimental results on real-world data, demonstrate that S-GGNs
exhibit superior convergence, robustness, and generalization, compared with
state-of-the-arts.
