Matrix-based Bayesian Network for efficient memory storage and flexible inference
Matrix-based Bayesian Network for efficient memory storage and flexible inference
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DOI：
10.1016/j.ress.2019.01.007
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发表时间：
2019-05-01
影响因子：
8.1
通讯作者：
Song, Junho
中科院分区：
文献类型：
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作者：
Byun, Ji-Eun;Zwirglmaier, Kilian;Song, Junho
对于由大量功能和统计相关组件组成的现实世界民用基础设施系统（例如运输系统或供水网络），贝叶斯网络 (BN) 可以成为概率推理的强大工具。在 BN 中，多个随机变量 (r.v.) 之间的统计关系通过有向无环图进行建模。 BN 中推理的复杂性不仅取决于 r.v. 的数量，还取决于图形结构。因此，即使 r.v. 的数量适中，标准 BN 技术的应用也可能变得不可行，因为事件集的大小随着 r.v. 的数量呈指数增长。此外，当离散 BN 节点的全面量化所需的穷举集变得难以处理时，只有近似推理算法是可行的，这不需要所有 BN 节点的完整（显式）描述。我们通过提出基于矩阵的贝叶斯网络（MBN）来解决离散 BN 中的这两个问题，该网络有助于联合概率质量函数的有效建模和灵活的推理。 MBN 是为精确和近似 BN 推断而开发的。通过数值算例证明了MBN的效率和适用性。支持源代码和数据可在 https://github.com/jieunbyun/GitHub-MBN-code 下载。
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.