Learning Graph Processes with Multiple Dynamical Models

Network-science related applications frequently deal with inference of spatio-temporal processes. Such inference tasks can be aided by a graph whose topology contributes to the underlying spatio-temporal dependencies. Contemporary approaches extrapolate dynamic processes relying on a fixed dynamical model, that is not adaptive to changes in the dynamics. Alleviating this limitation, the present work adopts a candidate set of graph-adaptive dynamical models with one active at any given time. Given partially observed nodal samples, a scalable Bayesian tracker is leveraged to infer the graph processes and learn the active dynamical model simultaneously in a data-driven fashion. The resulting algorithm is termed graph-adaptive interacting multiple dynamical models (Grad-IMDM). Numerical tests with synthetic and real data corroborate that the proposed Grad-IMDM is capable of tracking the graph processes and adapting to the dynamical model that best fits the data.

网络科学相关应用经常涉及时空过程的推断。此类推断任务可由一个图来辅助，该图的拓扑结构对潜在的时空依赖性有影响。当代方法依据固定的动态模型推断动态过程，该模型无法适应动态变化。为缓解这一局限，本研究采用一组图自适应动态模型候选集，在任何给定时间只有一个模型处于活动状态。给定部分观测到的节点样本，利用一种可扩展的贝叶斯跟踪器以数据驱动的方式同时推断图过程并学习活动的动态模型。由此产生的算法被称为图自适应交互多动态模型（Grad - IMDM）。对合成数据和真实数据的数值测试证实，所提出的Grad - IMDM能够跟踪图过程，并适应最适合数据的动态模型。