Penalized Maximum Likelihood Inference of Core-Periphery Networks
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核心—边缘网络的惩罚最大似然推断
- 研究问题
- 当独立连边等低阶约束不能再现核心—边缘网络中的楔形与三角结构时，如何兼顾似然拟合和高阶结构匹配？
- 方法与思路
- 作者在负对数似然中加入标准化楔形与三角偏差惩罚，校准单一调节参数，并构建混合约束的核心—边缘指数随机图模型。
- 材料陈述的贡献
- 摘要称，惩罚在模型正确设定时可关闭；新模型结合高阶结构公式与应用，描述异质度数和高阶结构丰富的核心。
- 阅读关注点
- 应核对惩罚校准能否区分抽样波动与误设、线性响应解释的范围，以及帕累托核心适应度假设和连边拟合代价。
- 阅读边界
- 本资料为 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出推断有效性的完整条件，银行网络应用不能直接推出系统性风险结论。
原文摘要
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.