论文标题
在加权网络中测试社区结构的信息理论限制
Information-theoretic Limits for Testing Community Structures in Weighted Networks
论文作者
论文摘要
社区检测是指将网络的节点聚集成组的问题。社区结构的现有推论方法主要集中于未加权（二进制）网络。尽管如此，许多现实世界的网络仍然是加权的，一种常见的做法是将加权网络二分为未加权的网络，该网络已知会导致信息丢失。关于后一种情况下假设检验的文献仍然缺失。在本文中，我们研究了测试加权网络中社区结构存在的问题。我们的贡献是三倍：（a）。我们使用（可能是无限的）指数族族来建模权重，并为存在一致的测试而得出尖锐的信息理论极限。在限制内，任何测试都是不一致的。超过极限，我们提出了一个有用的一致测试。 （b）。基于信息理论限制，我们提供了第一种形式的方式，可以在假设检验的背景下将二分法加权图丢失到未加权的图中所产生的信息丢失。 （c）。我们提出了几个新的且实际上有用的测试统计数据。模拟研究表明，所提出的测试的性能良好。最后，我们将提出的测试应用于动物社交网络。
Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted (binary) networks. Many real-world networks are nonetheless weighted and a common practice is to dichotomize a weighted network to an unweighted one which is known to result in information loss. Literature on hypothesis testing in the latter situation is still missing. In this paper, we study the problem of testing the existence of community structure in weighted networks. Our contributions are threefold: (a). We use the (possibly infinite-dimensional) exponential family to model the weights and derive the sharp information-theoretic limit for the existence of consistent test. Within the limit, any test is inconsistent; and beyond the limit, we propose a useful consistent test. (b). Based on the information-theoretic limits, we provide the first formal way to quantify the loss of information incurred by dichotomizing weighted graphs into unweighted graphs in the context of hypothesis testing. (c). We propose several new and practically useful test statistics. Simulation study show that the proposed tests have good performance. Finally, we apply the proposed tests to an animal social network.
