论文标题

空间网络合奏的信息理论

Information theory of spatial network ensembles

论文作者

Bianconi, Ginestra

论文摘要

本章对网络信息理论的最新发展进行了全面且独立的讨论。网络的最大熵模型是强制执行一组约束的最小偏置合奏,并用于许多应用程序中,以生成网络的零模型。在这里,通过区分微域和规范的合奏来介绍网络的最大熵集合,从而在强加了大量约束的情况下,揭示了这两类合奏的非等效性。非常普遍的网络数据还包括元数据描述节点的特征,例如它们在真实或抽象空间中的位置。节点的特征可以视为确定与每个链接相关的成本的潜在变量。具有潜在变量的最大熵网络合奏包括空间网络及其概括。在本章中,我们介绍了包括机场和铁路网络在内的运输网络案例。最大熵网络集合满足给定的一组约束。但是,传统方法并不能提供对此类约束的起源的任何见解。我们使用信息理论原理来找到网络经典信息理论框架中潜在变量的最佳分布。该理论解释了数据保证推理算法效率的数据的“祝福”。

This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are used in a number of application to produce null model of networks. Here maximum entropy ensembles of networks are introduced by distinguishing between microcanonical and canonical ensembles revealing the the non-equivalence of these two classes of ensembles in the case in which an extensive number of constraints is imposed. It is very common that network data includes also meta-data describing feature of the nodes such as their position in a real or in an abstract space. The features of the nodes can be treated as latent variables that determine the cost associated to each link. Maximum entropy network ensembles with latent variables include spatial networks and their generalisation. In this chapter we cover the case of transportation networks including airport and rail networks. Maximum entropy network ensemble satisfy a given set of constraints. However traditional approaches do not provide any insight on the origin of such constraints. We use information theory principles to find the optimal distribution of latent variables in the framework of the classical information theory of networks. This theory explains the "blessing of non-uniformity" of data guaranteeing the efficiency of inference algorithms.

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