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.
Abstract
In this work we develop statistical methodology to estimate and perform inference on subgraph densities using time-indexed, or dynamic network sequences. These estimates explicitly adjust for observation errors for the network edges, and have good theoretical properties as the size of the network grows. By specifying a stochastically evolving hidden Markov network model, we address 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. These new methods vastly expand the analysis of noisy networks to new data settings, as network replicates are commonly observed dynamically. The methodology is also extended to consider joint inference for subgraph densities at multiple time points, to facilitate formal statistical comparison of dynamic network snapshots.
In many research fields, there is an increased availability of network data arising as replicated networks. However, most statistical models for network data in the literature are designed for a single network. Among these, the Stochastic Block Model is arguably the most popular model to perform vertex clustering and community detection. We propose the Hierarchical Stochastic Block Model, a generalization of the SBM to the setting of replicated networks. This model uses a Hierarchical Pitman-Yor prior for the block allocation vector of each graph, and allows different networks to share the same latent blocks. The number of blocks in each graph and the overall number of blocks need not be specify by the practitioner, hence avoiding complicated model selection procedures. A novel MCMC algorithm to perform posterior inference is derived. To illustrate how the model is able to capture different levels of block sharing, the HSBM is fit to a co-authorship and a brain connectomic network.
Marco Battiston, Clement Lee· Statistics and computing· 0 citations
A generative model for temporal networks that jointly controls community evolution and dynamic node sets and is used as a benchmark to study the impact of the rate at which nodes join/leave the network on the performance of dynamic community detection algorithms.
Peijie Zhong, Raúl Mondragón, Richard Clegg· 0 citations
Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.
The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees and establishes nonparametric convergence rates in both block-model and Holder-smooth regimes.
We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish Gaussian approximation results for the maximum norm under finite-moment and sub-Weibull conditions, providing explicit conditions under which the dimension may increase with the network size. We also propose a high-dimensional network HAC covariance estimator and establish its convergence properties, yielding a feasible procedure for simultaneous inference. Simulation studies demonstrate favorable finite-sample performance of the proposed method. We apply the procedure to study how spillover effects vary with an index of network homophily by constructing confidence bands for the conditional spillover-effect function. The application reveals heterogeneity and local significance that would be obscured by conventional low-dimensional inference.
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.
Dan Han, Vicki Modisette, Tinghan Li et al.· 0 citations
