Problem
Research questions and friction points this paper is trying to address.
core-periphery networks
likelihood-based models
higher-order structures
triangles and wedges
Penalized Maximum Likelihood Inference of Core-Periphery Networks
🤖 AI Summary
该研究提出了一种基于惩罚似然与结构差异（PLSD）的方法，通过修正网络模型中的楔形和三角形偏差来更好地拟合核心-外围网络的高阶结构。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Penalized Likelihood with Structural Discrepancies (PLSD)
Exponential Random Graph Model (ERGM)
core-periphery networks
motif discrepancies
mixed-constraint maximum-entropy
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