AI 中文总结
本文以三个经验二部系统为研究对象，对比四种空模型的性能，发现空模型约束的统计后果需通过共现统计量的概率分布分析，为二部网络空模型的比较提供了新依据。
AI 中文摘要
投影二部网络的统计验证高度依赖于用于描述随机共现的空模型。尽管已提出多种空模型，但对它们的比较主要集中于其生成的验证骨干网络，而非构建背后的统计假设。本文比较了四种广泛使用的空模型：由Curveball算法生成的微正则配置模型、二部配置模型（BiCM）、二部部分配置模型（BiPCM）以及超几何近似，使用了比较基因组学、国际贸易和食品科学的三个经验二部系统。我们将从微正则二部配置模型获得的统计验证链接作为参考基准，评估其他三种模型的性能。核心结果是，放松空模型约束的统计后果不能仅从约束本身理解，而必须通过共现统计量诱导的概率分布进行分析。具体而言，期望和方差的综合行为很大程度上解释了观察到的统计验证骨干网络之间的差异。我们进一步推导了BiCM期望的主导阶稀疏近似，表明对超几何预测的首次修正由非投影层的度异质性控制。令人惊讶的是，尽管忽略了这种异质性，超几何模型仍能准确复现所有数据集上微正则系综的共现方差。我们的结果表明，空模型的比较不仅应依据其保留的约束，还应依据这些约束对检验统计量分布诱导的统计后果。
英文摘要
Statistical validation of projected bipartite networks depends critically on the null model adopted to describe random co-occurrences. Although several null models have been proposed, their comparison has mainly focused on the validated backbones they produce rather than on the statistical assumptions underlying their construction. Here we compare four widely used null models - the microcanonical configuration model generated by the Curveball algorithm, the Bipartite Configuration Model (BiCM), the Bipartite Partial Configuration Model (BiPCM), and the Hypergeometric approximation - using three empirical bipartite systems from comparative genomics, international trade and food science. We use the statistically validated links obtained from the microcanonical bipartite configuration model as the reference benchmark for assessing performances of the other three models. Our central result is that the statistical consequences of relaxing null-model constraints cannot be understood solely from the constraints themselves but must be analyzed through the probability distribution induced for the co-occurrence statistic. In particular, the combined behaviour of the expectation and variance largely explains the observed differences among the statistically validated backbones. We further derive a leading-order sparse approximation for the BiCM expectation, showing that the first correction to the Hypergeometric prediction is controlled by the degree heterogeneity of the non-projected layer. Surprisingly, despite neglecting this heterogeneity, the Hypergeometric model accurately reproduces the co-occurrence variance of the microcanonical ensemble across all datasets. Our results suggest that null models should be compared not only according to the constraints they preserve but also according to the statistical consequences that these constraints induce on the distribution of the test statistic.
Comments17 pages, 2 figures and 4 tables
