Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence network among the dimensions of multi-dimensional temporal processes is of high importance in disciplines where a high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multi-dimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method incausal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts knowledge.

翻译：霍克斯过程是一个特殊的时间点过程类别,显示了自然的因果关系概念,因为过去发生的事件可能会增加未来事件的概率。发现多维时间过程的维度之间的基本影响网络在高频数据要建模的学科中非常重要,例如在金融数据或地震数据中。本文探讨在多维的霍克斯过程中学习Granger-causal网络的问题。我们把这个问题当作一个示范选择任务,我们遵循最低描述长度(MDL)原则。此外,我们提议使用蒙特-卡洛方法进行基于MDL的推断,我们用它来解决我们的因果发现问题。我们将我们的算法与合成和现实世界金融数据的最新基线方法进行比较。合成实验表明,与数据规模的基线方法相比,我们的方法的因果发现具有优势。与G-7债券价格数据实验的结果与专家的知识是一致的。