模拟复杂系统中的时变相互作用：分数驱动的动态伊辛模型
Modelling time-varying interactions in complex systems: the Score Driven Kinetic Ising Model
摘要：
在分析现实世界的复杂系统时，一个常见的问题是元素之间的相互作用经常随着时间的推移而变化：这使得很难找到描述这种演变的最佳模型，并且可以从数据中估计，特别是当驱动机制未知时。在这里，我们提供了一个新的角度发展的模型随时间变化的相互作用引入了一个推广的著名的动力伊辛模型（KIM），一个最小的成对常数相互作用模型，已发现应用在多个科学学科。将动态的任意选择保持在最低限度并寻求信息理论最优性，分数驱动方法使我们能够使用简单的KIM显着增加可以从数据中提取的知识。特别是，我们首先确定一个参数，其值在给定的时间可以直接与当地的可预测性的动态。然后，我们介绍了一种方法来动态地学习这样的参数的值从数据，而不需要参数化地指定其动态。最后，我们扩展了我们的框架，以解开不同的来源（如内源性与外源性）的可预测性在实时。我们将我们的方法应用于几个复杂的系统，包括金融市场，时间（社会）网络，和神经元群体。我们的研究结果表明，分数驱动的KIM系统产生有见地的描述，允许预测预测准确性在实时，以及分离不同的组件的动态。这为广泛学科的数据分析提供了重大的方法改进。
英文摘要：
A common issue when analyzing real-world complex systems is that the interactions between the elements often change over time: this makes it difficult to find optimal models that describe this evolution and that can be estimated from data, particularly when the driving mechanisms are not known. Here we offer a new perspective on the development of models for time-varying interactions introducing a generalization of the well-known Kinetic Ising Model (KIM), a minimalistic pairwise constant interactions model which has found applications in multiple scientific disciplines. Keeping arbitrary choices of dynamics to a minimum and seeking information theoretical optimality, the Score-Driven methodology lets us significantly increase the knowledge that can be extracted from data using the simple KIM. In particular, we first identify a parameter whose value at a given time can be directly associated with the local predictability of the dynamics. Then we introduce a method to dynamically learn the value of such parameter from the data, without the need of specifying parametrically its dynamics. Finally, we extend our framework to disentangle different sources (e.g. endogenous vs exogenous) of predictability in real time. We apply our methodology to several complex systems including financial markets, temporal (social) networks, and neuronal populations. Our results show that the Score-Driven KIM produces insightful descriptions of the systems, allowing to predict forecasting accuracy in real time as well as to separate different components of the dynamics. This provides a significant methodological improvement for data analysis in a wide range of disciplines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
