Previous studies have demonstrated that encoding a Bayesian network into a
SAT formula and then performing weighted model counting using a backtracking
search algorithm can be an effective method for exact inference. In this paper,
we present techniques for improving this approach for Bayesian networks with
noisy-OR and noisy-MAX relations---two relations that are widely used in
practice as they can dramatically reduce the number of probabilities one needs
to specify. In particular, we present two SAT encodings for noisy-OR and two
encodings for noisy-MAX that exploit the structure or semantics of the
relations to improve both time and space efficiency, and we prove the
correctness of the encodings. We experimentally evaluated our techniques on
large-scale real and randomly generated Bayesian networks. On these benchmarks,
our techniques gave speedups of up to two orders of magnitude over the best
previous approaches for networks with noisy-OR/MAX relations and scaled up to
larger networks. As well, our techniques extend the weighted model counting
approach for exact inference to networks that were previously intractable for
the approach.

本文提出了使用两种 SAT 编码的噪声 OR 和两种编码的噪声 MAX 的技术，以提高 Bayesian 网络的精确推理。经过实验评估，我们的技术在具有噪声 OR/MAX 关系的网络中获得了最佳效果。

利用加权模型计数中的结构进行概率推断

Exploiting Structure in Weighted Model Counting Approaches to  Probabilistic Inference

The Noisy-Or model is convenient for describing a class of uncertain
relationships in Bayesian networks [Pearl 1988]. Pearl describes the Noisy-Or
model for Boolean variables. Here we generalize the model to nary input and
output variables and to arbitrary functions other than the Boolean OR function.
This generalization is a useful modeling aid for construction of Bayesian
networks. We illustrate with some examples including digital circuit diagnosis
and network reliability analysis.

本文介绍了 Noisy-Or 模型在 Bayesian 网络中的推广运用，用于多元输入输出变量及除布尔 OR 函数以外的任意函数的建模。同时，介绍了一些实例应用，包括数字电路诊断和网络可靠性分析。