Automatically Finding the Right Probabilities in Bayesian Networks

IF 4.5 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Bahar Salmani, J. Katoen
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引用次数: 1

Abstract

This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using proba- bilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques.
在贝叶斯网络中自动寻找正确概率
本文提出了对经典贝叶斯网络进行推理的替代技术,其中所有概率都是固定的,以及当这种网络中的条件概率表(cpt)包含符号参数而不是具体概率时的综合问题。关键思想是利用概率模型检验及其最近扩展到参数马尔可夫链的参数综合技术。为了实现这一点,贝叶斯网络被转换成马尔可夫链,它们的目标被映射到概率时间逻辑公式。为了精确推断,我们在各种贝叶斯网络基准上比较了概率模型检查和加权模型计数。我们对比了使用多终端二进制(又名:代数)决策图的符号模型检查和使用概率-双向句子决策图的符号推理,这是为贝叶斯网络量身定制的符号数据结构。对于参数设置,我们描述了如何将我们的技术用于各种综合问题,例如计算灵敏度函数(和值),简单和差分参数调谐以及比率参数调谐。我们的参数合成技术适用于可能出现在多个cpt中的任意多个可能相关的参数。这解除了文献中存在的限制,例如,对参数化cpt的数量,或对几个cpt之间的参数依赖性。在几个基准测试上的实验表明,我们的参数合成技术可以处理现有技术无法达到的贝叶斯网络(具有数百个未知参数)的参数合成。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Artificial Intelligence Research
Journal of Artificial Intelligence Research 工程技术-计算机:人工智能
CiteScore
9.60
自引率
4.00%
发文量
98
审稿时长
4 months
期刊介绍: JAIR(ISSN 1076 - 9757) covers all areas of artificial intelligence (AI), publishing refereed research articles, survey articles, and technical notes. Established in 1993 as one of the first electronic scientific journals, JAIR is indexed by INSPEC, Science Citation Index, and MathSciNet. JAIR reviews papers within approximately three months of submission and publishes accepted articles on the internet immediately upon receiving the final versions. JAIR articles are published for free distribution on the internet by the AI Access Foundation, and for purchase in bound volumes by AAAI Press.
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