论信息链接
On Information Links
摘要：
在与D. Bennequin，我们建议3向多元互信息的（负）最小值对应于Borromean链接，为提供链接数的概率类似物铺平了道路。这篇短文概括了二元变量情形下k-多元相互作用信息的极小值与k-Brunnian链的对应关系。在Jakulin和Bratko之后，联合概率定律的相关K-L发散的负性及其Kirkwood近似意味着阻碍局部分解为比k更低阶的相互作用，定义了局部分解的不一致性，逆转了Abramsky的上下文局部-全局关系。这些负k-链接提供了复杂k体相互作用系统或数据集中集体涌现的直接定义。
英文摘要：
In a joint work with D. Bennequin, we suggested that the (negative) minima of the 3-way multivariate mutual information correspond to Borromean links, paving the way for providing probabilistic analogs of linking numbers. This short note generalizes the correspondence of the minima of k-multivariate interaction information with k Brunnian links in the binary variable case. Following Jakulin and Bratko, the negativity of the associated K-L divergence of the joint probability law with its Kirkwood approximation implies an obstruction to local decomposition into lower order interactions than k, defining a local decomposition inconsistency that reverses Abramsky's contextuality local-global relation. Those negative k-links provide a straightforward definition of collective emergence in complex k-body interacting systems or dataset.
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