A key feature of information theory is its universality, as it can be applied to study a broad variety of complex systems. However, many information-theoretic measures can vary significantly even across systems with similar properties, making normalisation techniques essential for allowing meaningful comparisons across datasets. Inspired by the framework of Partial Information Decomposition (PID), here we introduce Null Models for Information Theory (NuMIT), a null model-based non-linear normalisation procedure which improves upon standard entropy-based normalisation approaches and overcomes their limitations. We provide practical implementations of the technique for systems with different statistics, and showcase the method on synthetic models and on human neuroimaging data. Our results demonstrate that NuMIT provides a robust and reliable tool to characterise complex systems of interest, allowing cross-dataset comparisons and providing a meaningful significance test for PID analyses.

翻译：信息理论的一个关键特征在于其普适性，因为它可被应用于研究各种复杂的系统。然而，许多信息论度量即使在具有相似性质的系统之间也可能存在显著差异，这使得归一化技术对于实现跨数据集的有意义比较至关重要。受部分信息分解（PID）框架的启发，本文引入了信息论零模型（NuMIT），这是一种基于零模型的非线性归一化方法，它改进了标准的基于熵的归一化方法并克服了其局限性。我们为该技术在不同统计特性的系统上提供了实际实现，并在合成模型和人类神经影像数据上展示了该方法。我们的结果表明，NuMIT为表征感兴趣的复杂系统提供了一个稳健可靠的工具，允许进行跨数据集比较，并为PID分析提供了有意义的显著性检验。