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.

翻译：本文提出随机Gumbel图网络（Stochastic Gumbel Graph Networks, S-GGNs）用于学习高维时间序列，其中观测维度通常存在空间相关性。为此，通过分别学习随机微分方程中的漂移项和扩散项，并借助Gumbel矩阵嵌入来捕捉观测随机性与空间相关性。特别地，这一新颖框架使我们能够研究S-GGNs中噪声项的隐式正则化效应。我们通过推导权重邻域内两个对应损失函数之间的差异，为所提出的S-GGNs提供了理论保证。进而采用Kuramoto模型生成数据，以比较这两个损失函数的海森矩阵（Hessian Matrix）的谱密度。在实际数据集上的实验结果表明，与现有最先进方法相比，S-GGNs在收敛性、鲁棒性和泛化能力方面均表现更优。