Matrix-based Bayesian Network for efficient memory storage and flexible inference

• Published in: Reliability engineering & system safety 2019-05, Vol.185, p.533-545
• Main Authors: Byun, Ji-Eun, Zwirglmaier, Kilian, Straub, Daniel, Song, Junho
• Format: Article
• Language: English
• Subjects: Algorithms; Approximate inference; Bayesian analysis; Bayesian Network; Complex systems; Data processing; Discrete Bayesian Network; Distribution management; Downloading; Exact inference; Learning; Mathematical models; Matrix-based modeling; Probabilistic inference; Random variables; Reliability engineering; Source code; Statistical analysis; Statistical inference; Transportation; Transportation networks; Transportation systems; Water distribution; Water engineering
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2019.01.007

•A new data structure for discrete Bayesian Network is proposed.•Both exact and approximate algorithms are developed for BN inference.•Existing BN inference methodologies are compatible with the proposed data structure.•Exact and approximate inferences of BNs are unified and generalized.•Numerical examples demonstrate the performance of the proposed methodology. For real-world civil infrastructure systems that consist of a large number of functionally and statistically dependent components, such as transportation systems or water distribution networks, the Bayesian Network (BN) can be a powerful tool for probabilistic inference. In a BN, the statistical relationship between multiple random variables (r.v.’s) is modeled through a directed acyclic graph. The complexity of inference in the BN depends not only on the number of r.v.’s, but also the graphical structure. As a consequence, the application of standard BN techniques may become infeasible even with a moderate number of r.v.’s as the size of an event set exponentially increases with the number of r.v.’s. Moreover, when the exhaustive set that is required for full quantification of a discrete BN node becomes intractably large, only approximate inference algorithms are feasible, which do not require the full (explicit) description of all BN nodes. We address both issues in discrete BNs by proposing a matrix-based Bayesian Network (MBN) that facilitates efficient modeling of joint probability mass functions and flexible inference. The MBN is developed for exact as well as approximate BN inference. The efficiency and applicability of the MBN are demonstrated by numerical examples. The supporting source code and data are available for download at https://github.com/jieunbyun/GitHub-MBN-code.