The Effects of Node Removal on Bayesian Network Resilience for ATM Network Transaction Vulnerabilities

Abstract

We investigate the evaluation of influence relationships in probabilistic graphical models, focusing on the impact of node removal (mutilation) within Bayesian networks. The central problem addressed is understanding how the joint probability distribution and influence structure among interconnected variables evolve when a subset of nodes is removed, an issue relevant to various real-world systems experiencing disruptions. We model these dynamics using Bayesian learning to provide insights into network resilience and dependencies. To explore these effects, we generate synthetic Bayesian network structures that are tree-like, sparse, and dense, each representing different real-world configurations found in machine learning, sensor networks, and financial modeling. Conditional Probability Distributions (CPDs) were assigned to nodes based on the Bernoulli distribution. The Kullback-Leibler (KL) divergence quantified the deviations in influence structures post-removal, with evaluation of structure recovery employing an exact inference technique. Our findings indicate that each network type exhibits distinct responses to node removal: tree-like structures stabilize quickly with increased data, sparse structures show higher sensitivity but recover efficiently, and dense structures offer robustness through redundancy, though they demand larger datasets. These findings have significant implication for optimizing complex systems, particularly those requiring resilient network architectures. As a real-world application, we model ATM transaction networks to analyze how the removal of ATMs (due to vandalism, load shedding, or maintenance) impacts transaction flows. Our results show that high-traffic ATMs serve as critical nodes, significantly influencing neighboring ATMs when removed. By applying Bayesian structure learning, we demonstrate that optimal ATM network configurations can be identified to minimize disruption and improve financial service resilience. This study contributes to the growing field of probabilistic graphical models by introducing a novel approach to understanding influence dynamics in mutilated networks. It provides practical insights and lays a foundation for further research into complex systems where node integrity and network stability are critical for decision-making and operational efficiency.