Dynamical Origins of Distribution Functions
Dynamical Origins of Distribution Functions
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DOI：
10.1145/3292500.3330842
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Chengxi Zang;Peng Cui;Wenwu Zhu;Fei Wang
中科院分区：
文献类型：
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作者：
Chengxi Zang;Peng Cui;Wenwu Zhu;Fei Wang
许多现实世界的问题本质上都是随时间演变的，例如疾病的进展，社交网络中帖子传播时的级联过程，或者气候的变化。表征这些复杂问题的观测数据通常只能在离散的时间戳上获得，这使得现有的分析这些问题的研究大多基于横截面分析。在本文中，我们试图通过一个动态系统来模拟这些随时间演化的现象，在不同的时间戳观察到的数据集是由这样一个动态系统产生的概率分布函数。我们提出了一个定理，它建立了一个由微分方程建模的动力系统和这个系统的横截面状态的分布函数（或生存函数）之间的数学关系。然后，我们开发了一个生存分析框架，学习微分方程的动力系统，从它的横截面状态。有了这样一个框架，我们就能够捕捉到一个进化系统的连续时间动态。我们验证了我们的框架在合成和真实世界的数据集。实验结果表明，我们的框架是能够准确地发现和捕捉各种数据分布的生成动态。我们的研究可能有助于科学发现真实的世界中复杂系统的未知动力学。
Many real-world problems are time-evolving in nature, such as the progression of diseases, the cascading process when a post is broadcasting in a social network, or the changing of climates. The observational data characterizing these complex problems are usually only available at discrete time stamps, this makes the existing research on analyzing these problems mostly based on a cross-sectional analysis. In this paper, we try to model these time-evolving phenomena by a dynamic system and the data sets observed at different time stamps are probability distribution functions generated by such a dynamic system. We propose a theorem which builds a mathematical relationship between a dynamical system modeled by differential equations and the distribution function (or survival function) of the cross-sectional states of this system. We then develop a survival analysis framework to learn the differential equations of a dynamical system from its cross-sectional states. With such a framework, we are able to capture the continuous-time dynamics of an evolutionary system.We validate our framework on both synthetic and real-world data sets. The experimental results show that our framework is able to discover and capture the generative dynamics of various data distributions accurately. Our study can potentially facilitate scientific discoveries of the unknown dynamics of complex systems in the real world.