发表机构
Università di Pisa; Università di Siena（比萨大学; 锡耶纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出PLSD方法，通过惩罚似然修正核心-边缘网络推断，兼顾高阶结构，并在模拟与真实网络数据中验证其有效性。
AI 中文摘要
基于似然的网络模型通常在链接独立性和低阶约束下进行拟合，而经验网络经常表现出系统性的高阶结构，如三角形和楔形，这些结构刻画了观察到的聚类模式。现实世界的核心-边缘网络，如银行间市场或航空运输系统，是关键的实例，其核心表现出复杂且非线性的特征。我们将带有结构差异的惩罚似然（PLSD）形式化为一种推断层面的修正，它在似然拟合与目标模体一致性之间进行权衡。PLSD在负对数似然上增加了对标准化楔形和三角形差异的惩罚，从而对似然曲面产生可控的扭曲，这种扭曲可以通过线性响应分析来解释。我们引入了一种针对唯一调优超参数的校准方法，当模型被正确指定时，该方法会关闭惩罚项，从而在这种情况下恢复最大似然估计。然后，我们引入了一个混合约束的最大熵核心-边缘指数随机图模型（ERGM），在帕累托分布的核心适应度下推导出无条件的半封闭模体公式，并通过重尾分布的大跳跃机制解释稀疏区域的标度行为。最后，我们通过玩具随机块模型的蒙特卡洛模拟，以及将新颖的核心-边缘ERGM应用于每周eMID银行间网络（2009-2015年）和每月美国航空交通网络（1991-2000年），来验证PLSD推断方法。我们表明，PLSD描述的核心不仅密集，而且高阶丰富，并捕捉了观察到的异质度分布以及楔形和三角形的过度表达，其链接级成本与模型误设定成比例。
英文摘要
Likelihood-based network models are often fitted under links' independence and low-order constraints, while empirical networks frequently exhibit systematic higher-order structures such as triangles and wedges, characterizing the observed clustering patterns. Real-world core-periphery networks such as the interbank market or the air transportation system represent key examples, with cores displaying complex and nonlinear features. We formalize Penalized Likelihood with Structural Discrepancies (PLSD) as an inference-level correction that trades likelihood fit for agreement with targeted motifs. PLSD augments the negative log-likelihood with a penalty on standardized wedge and triangle discrepancies, yielding a controlled distortion of the likelihood surface that can be interpreted through a linear response analysis. A calibration approach for the unique tuning hyperparameter is introduced to turn off the penalization term when the model is correctly specified, thereby recovering maximum-likelihood estimation in that case. We then introduce a mixed-constraint maximum-entropy core-periphery Exponential Random Graph Model (ERGM), derive unconditional semi-closed motif formulas under Pareto-distributed core fitness, and interpret sparse-regime scaling through a big-jump mechanism for heavy-tailed distributions. We finally corroborate the PLSD inference methodology both with Monte Carlo simulations of a toy stochastic block model and by applying the novel core-periphery ERGM to weekly eMID interbank networks (2009-2015) and monthly US air traffic networks (1991-2000). We show that PLSD describes cores that are not only dense but also higher-order-rich and captures the observed heterogeneous degree distributions and the overexpression of wedges and triangles, at a link-level cost proportional to the model misspecification.
Comments29 pages, 21 figures. Code available at https://github.com/antoniomosca27/core-periphery-us-air-plsd
