经验网络随机块模型拟合质量的系统评价
Systematic assessment of the quality of fit of the stochastic block model for empirical networks
摘要：
我们对随机块模型（SBM）的拟合质量进行了系统的分析，该模型适用于275个经验网络，这些网络跨越了广泛的领域和数量级。我们采用后验预测模型检查作为评估拟合质量的标准，根据一组网络描述符，将推断模型生成的网络与经验网络进行比较。我们观察到，SBM是能够提供一个准确的描述大多数网络考虑，但不饱和的所有建模要求。特别是，具有大直径和慢混合随机游动的网络往往不能很好地用SBM描述。然而，与通常的假设相反，在许多情况下，具有高丰度三角形的网络可以很好地由SBM描述。我们证明，简单的网络描述符可以用来评估是否SBM可以提供足够准确的表示，可能指向可能的模型扩展，可以系统地提高这类模型的表达能力。
英文摘要：
We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.
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