网络中的度分布：超越幂律
Degree distributions in networks: beyond the power law
AI总结：
针对幂律拟合网络度分布时阈值选择不确定及模型充分性问题，提出结合广义帕累托与Zipf-polylog分布的混合建模框架，嵌入贝叶斯模型选择，实现良好拟合与阈值不确定性量化。
摘要：
幂律在描述计数现象（如网络度和词频）时非常有用。凭借单一参数，它捕捉了频率在对数-对数尺度上呈线性的主要特征。然而，对幂律一直存在批评，例如需要预先选择阈值而未量化其不确定性，幂律本身可能不充分，以及需要后续假设检验来确定数据是否可能来自幂律。我们提出了一个建模框架，结合了幂律的两种不同推广，即广义帕累托分布和Zipf-polylog分布，以解决这些问题。所提出的混合分布被证明能很好地拟合数据，并以自然的方式量化阈值不确定性。嵌入贝叶斯推断算法中的模型选择步骤进一步回答了幂律是否充分的问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
