Information Decomposition and Synergy
Information Decomposition and Synergy
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DOI：
10.3390/e17053501
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发表时间：
2015-05-01
期刊：
影响因子：
2.7
通讯作者：
Rauh, Johannes
中科院分区：
文献类型：
--
作者：
Olbrich, Eckehard;Bertschinger, Nils;Rauh, Johannes
最近，一系列的论文讨论了将两个随机变量的信息分解为共享信息、唯一信息和协同信息的问题。提出了若干措施，但仍未达成协商一致意见。在这里，我们将这些建议与一种旧的方法进行比较，该方法基于仅包含k阶相互作用的指数族上的投影来定义协同信息。我们表明，如果要求所有项总是非负的（局部正性），这些度量与分解为唯一、共享和协同信息是不兼容的。我们说明了多元高斯函数的两种度量之间的差异。
Recently, a series of papers addressed the problem of decomposing the information of two random variables into shared information, unique information and synergistic information. Several measures were proposed, although still no consensus has been reached. Here, we compare these proposals with an older approach to define synergistic information based on the projections on exponential families containing only up to k-th order interactions. We show that these measures are not compatible with a decomposition into unique, shared and synergistic information if one requires that all terms are always non-negative (local positivity). We illustrate the difference between the two measures for multivariate Gaussians.