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.

该论文提出了一种基于 Gumbel 图网络的随机模型，能够学习高维度时间序列，捕捉随机性和空间相关性，通过Kuramoto的模型比较了两个损失函数的Hessian矩阵，实验证明该模型在收敛性、稳健性和泛化性方面都具有优势。

利用图神经网络将随机动态系统学习作为隐式正则化