Scuola Normale Superiore, p. dei Cavalieri 7, 56126, Pisa, Italy.
UZH Blockchain Center, University of Zürich, Rämistrasse 71, 8006, Zürich, Switzerland.
Sci Rep. 2022 Nov 11;12(1):19339. doi: 10.1038/s41598-022-23770-0.
A common issue when analyzing real-world complex systems is that the interactions between their elements often change over time. Here we propose a new modeling approach for time-varying interactions generalising the well-known Kinetic Ising Model, a minimalistic pairwise constant interactions model which has found applications in several scientific disciplines. Keeping arbitrary choices of dynamics to a minimum and seeking information theoretical optimality, the Score-Driven methodology allows to extract from data and interpret the presence of temporal patterns describing time-varying interactions. We identify a parameter whose value at a given time can be directly associated with the local predictability of the dynamics and we introduce a method to dynamically learn its value from the data, without specifying parametrically the system's dynamics. We extend our framework to disentangle different sources (e.g. endogenous vs exogenous) of predictability in real time, and show how our methodology applies to a variety of complex systems such as financial markets, temporal (social) networks, and neuronal populations.
在分析现实世界中的复杂系统时，一个常见的问题是其元素之间的相互作用往往随时间而变化。在这里，我们提出了一种新的建模方法来处理时变相互作用，该方法推广了著名的动力学伊辛模型（Kinetic Ising Model），这是一个最小的、基于对相互作用的简单假设的模型，已经在多个科学领域得到了应用。通过保持对动力学的任意选择最小化，并寻求信息理论的最优性，得分驱动方法可以从数据中提取并解释描述时变相互作用的时间模式的存在。我们确定了一个参数，其在给定时间的值可以直接与动力学的局部可预测性相关联，并且我们引入了一种从数据中动态学习其值的方法，而无需参数化地指定系统的动力学。我们将我们的框架扩展到实时分离不同来源（例如，内源性与外源性）的可预测性，并展示了我们的方法如何应用于各种复杂系统，如金融市场、时间（社会）网络和神经元群体。
