Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone.
Multiscale Partial Information Decomposition of Dynamic Processes with Short and Long-range correlations: Theory and Application to Cardiovascular Control
Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'
University College London（伦敦大学学院）；Inria（法国国家信息与自动化研究所）；Google Research（谷歌研究院）；London School of Economics and Political Science（伦敦政治经济学院）；University of Oxford（牛津大学）
The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal
在多元系统中获得有意义的统计依赖性的定量描述是一个困难的开放性问题。部分信息分解（Partial Information Decomposition，PID）是将目标变量的互信息（Mutual Information，MI）分解为预测变量的不同子集中冗余、唯一和协同的分量。在这里，我们建议将PID的优雅形式主义应用于多变量熵，从而产生部分熵分解（PED）。我们实现了PED的熵冗余度测量的基础上逐点常见的代数，一个自然的定义，这是密切相关的MI的定义。我们展示了这种方法可以揭示二元与三元生成结构的多变量系统是无法区分的经典香农措施。熵的观点还表明，错误信息是协同熵，因此，MI本身包括冗余和协同效应。我们在两个预测PED和MI之间的关系，并推导出两种替代的信息分解，我们说明了几个示例系统。这表明，在熵方面，单变量预测MI是不是一个适当的子集的联合MI，我们建议这个以前未认识到的事实部分解释了为什么获得一致的PID已被证明是困难的。PED还允许单独量化机械冗余（与系统功能相关）与源冗余（由输入之间的依赖关系引起）;这是一个现有方法无法解决的重要区别。PED提供的新视角有助于澄清PID方法遇到的一些困难，由此产生的分解为广泛的应用领域的实际数据分析提供了有用的工具。
Multivariate Poisson intensity estimation via low-rank tensor decomposition
Auburn University（奥本大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, San Diego（加州大学圣迭戈分校）
