Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data

Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient inference algorithms due to the high computational cost of inferring many model parameters based on random sampling. Although Markov Chain Monte Carlo (MCMC) algorithms have been widely used for Bayesian inference, sampling using this class of algorithms is time-consuming for applications with large-scale data and time-sensitive decision-making, partially due to the non-conjugacy of many models. To overcome this limitation, this research develops an approximate Gibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining the inference accuracy. In the proposed sampler, the data likelihood is approximated with Gaussian distribution such that the conditional posterior of the coefficients has a closed-form solution. Numerical experiments using real and synthetic datasets with small and large counts demonstrate the superior performance of AGS in comparison to the state-of-the-art sampling algorithm, especially for large datasets.

A Bayesian Approach to Reconstructing Interdependent Infrastructure Networks from Cascading Failures

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.

Reconstructing Sparse Illicit Supply Networks: A Case Study of Multiplex Drug Trafficking Networks

The network structure provides critical information for law enforcement agencies to develop effective strategies to interdict illicit supply networks. However, the complete structure of covert networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of covert networks. In this paper, we work on real-world multiplex drug trafficking networks extracted from an investigation report. A statistical approach built on the EM algorithm (DegEM) as well as other methods based on structural similarity are applied to reconstruct the multiplex drug trafficking network given different fractions of observed nodes and links. It is found that DegEM approach achieves the best predictive performance in terms of several accuracy metrics. Meanwhile, structural similarity-based methods perform poorly in reconstructing the drug trafficking networks due to the sparsity of links between nodes in the network. The inferred multiplex networks can be leveraged to (i) inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve the reconstruction accuracy and (ii) develop more effective interdiction strategies.