Unified framework for information integration based on information geometry
Unified framework for information integration based on information geometry
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DOI：
10.1073/pnas.1603583113
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发表时间：
2016-12-20
影响因子：
11.1
通讯作者：
Amari, Shun-ichi
中科院分区：
文献类型：
--
作者：
Oizumi, Masafumi;Tsuchiya, Naotsugu;Amari, Shun-ichi
因果影响评估是一个普遍存在的重要课题，跨越不同的研究领域。从意识研究中得出，整合信息是一种衡量标准，它将整合定义为元素之间因果影响的程度。虽然元素之间的成对因果关系可以用现有的方法量化，但量化许多元素之间的多重影响带来了两个主要的数学困难。首先，如果每个影响以基于部分的方式单独量化，然后简单地求和，则由于影响之间的相互依赖性而发生高估。其次，很难在避免非因果混杂影响的同时隔离因果影响。为了解决这些困难，我们提出了一个基于信息几何的理论框架，以量化的多个因果影响与整体的方法。我们得到一个综合信息的措施，这是几何解释为一个系统的实际概率分布和近似的概率分布之间的分歧，其中元素之间的因果影响是统计断开。这个框架提供了直观的几何解释，协调各种信息理论的措施，在一个统一的方式，包括互信息，传递熵，随机相互作用，和综合信息，其中每一个的特点是如何因果关系的影响是断开的。除了对意识的数学评估外，我们的框架应该有助于以完整和分层的方式分析复杂系统中的因果关系。
Assessment of causal influences is a ubiquitous and important subject across diverse research fields. Drawn from consciousness studies, integrated information is a measure that defines integration as the degree of causal influences among elements. Whereas pairwise causal influences between elements can be quantified with existing methods, quantifying multiple influences among many elements poses two major mathematical difficulties. First, overestimation occurs due to interdependence among influences if each influence is separately quantified in a part-based manner and then simply summed over. Second, it is difficult to isolate causal influences while avoiding noncausal confounding influences. To resolve these difficulties, we propose a theoretical framework based on information geometry for the quantification of multiple causal influences with a holistic approach. We derive a measure of integrated information, which is geometrically interpreted as the divergence between the actual probability distribution of a system and an approximated probability distribution where causal influences among elements are statistically disconnected. This framework provides intuitive geometric interpretations harmonizing various information theoretic measures in a unified manner, including mutual information, transfer entropy, stochastic interaction, and integrated information, each of which is characterized by how causal influences are disconnected. In addition to the mathematical assessment of consciousness, our framework should help to analyze causal relationships in complex systems in a complete and hierarchical manner.