This work introduces BERGM Elastic Net, an adaptive empirical-Bayes approach that combines lasso shrinkage with ridge stabilization in a Bayesian ERGM that is developed for over-specified network models containing many related structural and covariate effects.
Abstract
Exponential random graph models (ERGMs) describe dependence among network ties, but inference becomes difficult when the likelihood is intractable and candidate network statistics are strongly correlated. We introduce BERGM Elastic Net, an adaptive empirical-Bayes approach that combines lasso shrinkage with ridge stabilization in a Bayesian ERGM. A latent-variable formulation supports approximate exchange sampling, while empirical-Bayes updates adapt the amount of regularization to the observed network. We connect the proposed prior to elastic-net penalized likelihood and clarify the interpretation of thresholded reporting and coefficient grouping. The method is developed for over-specified network models containing many related structural and covariate effects.
This work derives Weibull, Gumbel, and Exponential penalties that approximate \(\ell_0\) penalization and calibrate their hyperparameters to each dataset's noise floor, and formally proves the asymptotic properties of their static forms.
A. Christensen, Jeongwon Choi, Hao-Yi Yang et al.· 0 citations
By specifying a stochastically evolving hidden Markov network model, this work addresses two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots.
Complex-network analysis describes risk relations, whereas Bayesian networks (BNs) support probabilistic updating and scenario analysis. We propose a network-to-prior interface that converts semantic roles, normalized mutual information, communities, and bridge participation into a feasible edge domain and data-revisab...
For clique counts, a multivariate quantitative normal approximation result through the Malliavin–Stein method is established and distributional convergence based on a central limit theorem for sequences of associated random variables is obtained.
Christian Hirsch, Raphael Lachièze-Rey, Takashi Owada· Advances in Applied Probabil...· 0 citations
A novel method of inference for network-dependent high-dimensional random vectors is developed, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods.
It is shown 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.
A. Mosca, Piero Mazzarisi· 0 citations
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