论文标题
网络中的学位分配：超越权力法
Degree distributions in networks: beyond the power law
论文作者
论文摘要
权力定律可用于描述计数现象，例如网络学位和单词频率。使用单个参数，它捕获了频率在日志量表上是线性的主要功能。然而，例如对权力法的批评，例如，如果不量化其不确定性，就需要预先选择一个阈值，而权力法只是不足的，并且随后的假设检验需要确定数据是否可以来自权力法。我们提出了一个建模框架，该框架结合了功率定律的两个不同的概括，即广义的帕累托分布和Zipf-Polylog分布，以解决这些问题。所提出的混合物分布显示出可以很好地拟合数据并以自然方式量化阈值不确定性。嵌入在贝叶斯推理算法中的模型选择步骤进一步回答了权力定律是否足够的问题。
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been criticisms of the power law, for example that a threshold needs to be pre-selected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modelling framework that combines two different generalisations of the power law, namely the generalised Pareto distribution and the Zipf-polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.
