互信息增益与信息损失双重分解的冗余与协同
Redundancy and synergy in dual decompositions of mutual information gain and information loss
摘要：
Williams和Beer（2010）提出了一种基于信息增益格的非负互信息分解，它允许将一组变量包含的关于另一个变量的信息分离成可解释为一个变量的唯一信息的分量，或冗余和协同分量。在这项工作中，我们扩展了Williams和Beer（2010）的框架，专注于支撑分解的格。我们推广了可构造格的类型，并研究了不同格中项之间的关系，例如二元和三元分解。我们指出，在信息增益格，冗余组件是不变的分解，但独特的和协同组件是分解相关的。利用不同格之间的连接，我们提出了一个程序来构建，在一般的多元情况下，信息分解的措施，协同或独特的信息。我们引入了另一种类型的互信息分解的基础上的信息损失格，与交换相对于增益格的冗余和协同组件的作用和不变性。我们研究了信息增益和信息损失格之间的对应关系，我们定义了对偶分解，允许克服不变和分解依赖组件之间的内在不对称性，这阻碍了协同和冗余的一致联合表征。
英文摘要：
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of information gain lattices, which allows separating the information that a set of variables contains about another into components interpretable as the unique information of one variable, or redundant and synergy components. In this work we extend the framework of Williams and Beer (2010) focusing on the lattices that underpin the decomposition. We generalize the type of constructible lattices and examine the relations between the terms in different lattices, for example relating bivariate and trivariate decompositions. We point out that, in information gain lattices, redundancy components are invariant across decompositions, but unique and synergy components are decomposition-dependent. Exploiting the connection between different lattices we propose a procedure to construct, in the general multivariate case, information decompositions from measures of synergy or unique information. We introduce an alternative type of mutual information decompositions based on information loss lattices, with the role and invariance properties of redundancy and synergy components exchanged with respect to gain lattices. We study the correspondence between information gain and information loss lattices and we define dual decompositions that allow overcoming the intrinsic asymmetry between invariant and decomposition-dependent components, which hinders the consistent joint characterization of synergy and redundancy.
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