Confidence Analysis for Nuclear Arms Control: SMT Abstractions of Bayesian Belief Networks
Confidence Analysis for Nuclear Arms Control: SMT Abstractions of Bayesian Belief Networks
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核军控置信度分析：贝叶斯置信网络的 SMT 抽象
DOI：
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发表时间：
2015
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通讯作者：
T. Plant
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作者：
Paul Beaumont;Neil Evans;M. Huth;T. Plant
原则上如何以双方或多方信任的可核查方式削减军备是一个困难但重要的问题。希望从事这类军备控制核查活动的国家和组织需要能够设计程序和控制机制，以反映它们的信任假设，并让它们计算相关的信任度。至关重要的是，他们还需要一些方法，在几乎没有背景数据的情况下，可靠地评估他们在这种计算出的信任度中的信心。我们用我们所说的受限贝叶斯信念网络cBBN来模拟军备控制核查情景。CBBN通过象征性地表示关于BBN未表示的概率和特定于场景的约束的不确定性来表示一组贝叶斯信念网络。我们表明，这种对BBN的抽象可以很好地缓解先验数据的缺乏。具体地说，我们描述了cBBN如何在可满足性模理论SMT求解器中具有忠实的表示，并且这些表示开辟了自动评估我们对cBBN所表示的信任度的置信度的新方法。此外，我们还展示了如何执行cBBN的符号敏感度分析，以及如何计算决策感兴趣的欠指定概率的全局最优值。SMT求解还使我们能够评估我们在同一场景的两个cBBN中的相对置信度，其中这些模型可能共享一些信息，但在不同的抽象级别表达了场景的某些方面。
How to reduce, in principle, arms in a verifiable manner that is trusted by two or more parties is a hard but important problem. Nations and organisations that wish to engage in such arms control verification activities need to be able to design procedures and control mechanisms that capture their trust assumptions and let them compute pertinent degrees of belief. Crucially, they also will need methods for reliably assessing their confidence in such computed degrees of belief in situations with little or no contextual data. We model an arms control verification scenario with what we call constrained Bayesian Belief Networks cBBN. A cBBN represents a set of Bayesian Belief Networks by symbolically expressing uncertainty about probabilities and scenario-specific constraints that are not represented by a BBN. We show that this abstraction of BBNs can mitigate well against the lack of prior data. Specifically, we describe how cBBNs have faithful representations within a Satisfiability Modulo Theory SMT solver, and that these representations open up new ways of automatically assessing the confidence that we may have in the degrees of belief represented by cBBNs. Furthermore, we show how to perform symbolic sensitivity analyses of cBBNs, and how to compute global optima of under-specified probabilities of particular interest to decision making. SMT solving also enables us to assess the relative confidence we have in two cBBNs of the same scenario, where these models may share some information but express some aspects of the scenario at different levels of abstraction.