用逐点共变度量样本中的多元冗余信息
Measuring multivariate redundant information with pointwise common change in surprisal
摘要：
如何正确量化冗余信息的问题是一个悬而未决的问题，一直是最近许多研究的主题。冗余信息是指关于两个或更多个预测变量Xi共有的目标变量S的信息。它可以被认为是量化重叠的信息内容或Xi之间S表示的相似性。我们提出了一种新的冗余度的措施，措施之间共享的局部或逐点水平的变量之间的共同变化。我们提供了一个博弈论的操作定义的唯一信息，并使用此来获得用于获得最大熵分布的约束。然后，通过仅计数那些允许作为冗余信息的明确解释的局部共信息项，从该最大熵分布计算冗余度。我们展示了如何可以使用这种冗余措施的框架内的部分信息分解（PID）给一个直观的分解的多元互信息冗余，独特和协同的贡献。我们比较我们的新措施，现有的方法在一系列的示例系统，包括连续高斯变量。提供了测量的Matlab代码，包括所有考虑的例子。
英文摘要：
The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables Xi. It can be thought of as quantifying overlapping information content or similarities in the representation of S between the Xi. We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples.
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