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Maximizing Multivariate Information With Error-Correcting Codes

机译：最大化具有纠错码的多变量信息

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摘要

Multivariate mutual information provides a conceptual framework for characterizing higher-order interactions in complex systems. Two well-known measures of multivariate information-total correlation and dual total correlation-admit a spectrum of measures with varying sensitivity to intermediate orders of dependence. Unfortunately, these intermediate measures have not received much attention due to their opaque representation of information. Here we draw on results from matroid theory to show that these measures are closely related to error-correcting codes. This connection allows us to derive the class of global maximizers for each measure, which coincide with maximum distance separable codes of order $k$ . In addition to deepening the understanding of these measures and multivariate information more generally, we use these results to show that previously proposed bounds on information geometric quantities are met with equality for the global min and max.
机译：多变量互信息提供了一种概念框架，用于在复杂系统中表征高阶交互。两种众所周知的多变量信息 - 总相关性和双总相关措施 - 承认具有不同依赖性的敏感性的频谱。不幸的是，由于他们不透明的信息表示，这些中间措施并未受到大量关注。在这里，我们借鉴了Matroid理论的结果，表明这些措施与纠错码密切相关。此连接允许我们为每个度量派生全局最大化器的类，这与最大距离可分离的订单$ k $的码相一致。除了更好地深化这些措施和多变量信息之外，我们使用这些结果表明，以全球最小值和最大的平等满足先前提出的信息几何数量的界限。

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