Tsur Dor, Permuter Haim
School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel.
Entropy (Basel). 2025 Mar 28;27(4):357. doi: 10.3390/e27040357.
Despite the widespread use of information measures in analyzing probabilistic systems, effective visualization tools for understanding complex dependencies in sequential data are scarce. In this work, we introduce the information matrix (InfoMat), a novel and intuitive matrix representation of information transfer in sequential systems. InfoMat provides a structured visual perspective on mutual information decompositions, enabling the discovery of new relationships between sequential information measures and enhancing interpretability in time series data analytics. We demonstrate how InfoMat captures key sequential information measures, such as directed information and transfer entropy. To facilitate its application in real-world datasets, we propose both an efficient Gaussian mutual information estimator and a neural InfoMat estimator based on masked autoregressive flows to model more complex dependencies. These estimators make InfoMat a valuable tool for uncovering hidden patterns in data analytics applications, encompassing neuroscience, finance, communication systems, and machine learning. We further illustrate the utility of InfoMat in visualizing information flow in real-world sequential physiological data analysis and in visualizing information flow in communication channels under various coding schemes. By mapping visual patterns in InfoMat to various modes of dependence structures, we provide a data-driven framework for analyzing causal relationships and temporal interactions. InfoMat thus serves as both a theoretical and empirical tool for data-driven decision making, bridging the gap between information theory and applied data analytics.
尽管信息度量在概率系统分析中得到了广泛应用，但用于理解序列数据中复杂依赖关系的有效可视化工具却很匮乏。在这项工作中，我们引入了信息矩阵（InfoMat），这是一种新颖且直观的序列系统中信息传递的矩阵表示。InfoMat为互信息分解提供了结构化的可视化视角，能够发现序列信息度量之间的新关系，并增强时间序列数据分析中的可解释性。我们展示了InfoMat如何捕捉关键的序列信息度量，如定向信息和转移熵。为了便于其在现实世界数据集的应用，我们提出了一种基于掩码自回归流的高效高斯互信息估计器和一种神经InfoMat估计器，以对更复杂的依赖关系进行建模。这些估计器使InfoMat成为在数据分析应用中发现隐藏模式的宝贵工具，涵盖神经科学、金融、通信系统和机器学习等领域。我们进一步说明了InfoMat在可视化现实世界序列生理数据分析中的信息流以及在各种编码方案下可视化通信信道中的信息流方面的效用。通过将InfoMat中的视觉模式映射到各种依赖结构模式，我们提供了一个用于分析因果关系和时间交互的数据驱动框架。因此，InfoMat既是数据驱动决策的理论工具，也是实证工具，弥合了信息理论与应用数据分析之间的差距。
