Optimal Causation Entropy (oCSE) is a robust causal network modeling technique that reveals causal networks from dynamical systems and coupled oscillators, distinguishing direct from indirect paths. CausationEntropy is a Python package that implements oCSE and several of its significant optimizations and methodological extensions. In this paper, we introduce the version 1.1 release of CausationEntropy, which includes new synthetic data generators, plotting tools, and several advanced information-theoretical causal network discovery algorithms with criteria for estimating Gaussian, k-nearest neighbors (kNN), geometric k-nearest neighbors (geometric-kNN), kernel density (KDE) and Poisson entropic estimators. The package is easy to install from the PyPi software repository, is thoroughly documented, supplemented with extensive code examples, and is modularly structured to support future additions. The entire codebase is released under the MIT license and is available on GitHub and through PyPi Repository. We expect this package to serve as a benchmark tool for causal discovery in complex dynamical systems.

翻译：最优因果熵（oCSE）是一种稳健的因果网络建模技术，可从动态系统和耦合振荡器中揭示因果网络，区分直接路径与间接路径。CausationEntropy是一个实现了oCSE及其若干重要优化与方法扩展的Python软件包。本文介绍CausationEntropy 1.1版本，该版本包含新的合成数据生成器、绘图工具，以及多种基于信息理论的高级因果网络发现算法，这些算法具备估计高斯分布、k近邻（kNN）、几何k近邻（geometric-kNN）、核密度估计（KDE）和泊松熵估计器的判据标准。该软件包可通过PyPi软件仓库便捷安装，具备完整文档说明和大量代码示例，采用模块化结构以支持未来功能扩展。全部代码基于MIT许可证发布，可通过GitHub和PyPi仓库获取。我们预期该工具包将成为复杂动态系统中因果发现的基准测试工具。