Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a central location, limiting their applications in scenarios where data is gathered by different agents. In this paper, we propose a distributed sparse inverse covariance algorithm to learn the network structure (i.e., dependencies among observed entities) in real-time from data collected by distributed agents. Our approach is built on an online graphical alternating minimization algorithm, augmented with a consensus term that allows agents to learn the desired structure cooperatively. We allow the system designer to select the number of communication rounds and optimization steps per data point. We characterize the rate of convergence of our algorithm and provide simulations on synthetic datasets.

翻译：从时间序列数据中学习不同实体之间的关系在许多应用中至关重要。 已经研究了高斯图形模型,以推断这些关系。 但是,现有的算法在中央地点分批处理数据,在数据由不同代理人收集的情况下限制其应用。 在本文中,我们建议采用分散的零散反常变算法,从分布代理人收集的数据中实时学习网络结构(即观测到的实体之间的依赖性)。 我们的方法建立在在线图形交替最小化算法上,并辅之以一个协商一致的术语,使代理人能够合作学习理想的结构。 我们允许系统设计者选择通信周期的数目和每个数据点的最佳步骤。 我们确定我们的算法的趋同率,并提供合成数据集的模拟。