论文标题
在事件链中发现外源性和内源性因素的统计物理学
The statistical physics of discovering exogenous and endogenous factors in a chain of events
论文作者
论文摘要
事件的发生不仅受环境变化的影响，而且还会受到系统中发生的事件的促进。在这里，我们开发了一种从一系列事件发生时间估算此类外部和内在因素的方法。分析是使用分别代表外源波动和内源性链反应机制的模型进行分析的。该模型通过最大程度地减少自由能而适合给定的数据集，该模型利用了统计物理和路径综合方法。由于事件发生的过程是随机的，因此参数估计不可避免地伴随着错误，并且最终可能会发生外源性和内源性因素，即使使用最佳估计器也无法捕获。根据是否检测到各自的因素，我们获得了四个分类的制度。通过将分析方法应用于社交网络服务中的实时辩论序列，我们观察到，估计的外源性和内源性因素分别接近第一个评论和后续评论。此方法是一般的，适用于各种数据，我们提供了一个申请程序，任何人都可以分析任何系列事件时间。
Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of event-occurrence times. The analysis is performed using a model that combines the inhomogeneous Poisson process and the Hawkes process, which represent exogenous fluctuations and endogenous chain-reaction mechanisms, respectively. The model is fit to a given dataset by minimizing the free energy, for which statistical physics and a path-integral method are utilized. Because the process of event occurrence is stochastic, parameter estimation is inevitably accompanied by errors, and it can ultimately occur that exogenous and endogenous factors cannot be captured even with the best estimator. We obtained four regimes categorized according to whether respective factors are detected. By applying the analytical method to real time series of debate in a social-networking service, we have observed that the estimated exogenous and endogenous factors are close to the first comments and the follow-up comments, respectively. This method is general and applicable to a variety of data, and we have provided an application program, by which anyone can analyze any series of event times.
