Conditional independence encoded in Bayesian networks (BNs) avoids combinatorial explosion on the number of variables. However, BNs are still subject to exponential growth of space and inference time on the number of causes per effect variable in conditional probability tables. A number of space-efficient local models exist that allow efficient encoding of dependency between an effect and its causes, and can also be exploited for improved inference efficiency. We focus on the Nonimpeding Noisy-AND Tree (NIN-AND Tree or NAT) models because of multiple merits. We present a novel framework, trans-causalization of NAT-modeled BNs, by which causal independence embedded in NAT models is exploited for more efficient inference. We show that trans-causalization is exact and yields polynomial space complexity. We demonstrate significant efficiency gain on inference based on lazy propagation and sum–product networks.

中文翻译：

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跨因果 NAT 模型贝叶斯网络


贝叶斯网络 (BN) 中编码的条件独立性避免了变量数量的组合爆炸。然而，BN 仍然受到条件概率表中每个结果变量的原因数量的空间和推理时间的指数增长的影响。存在许多节省空间的局部模型，它们允许对效果与其原因之间的依赖性进行有效编码，并且还可以用于提高推理效率。由于多种优点，我们重点关注无阻碍噪声与树（NIN-AND 树或 NAT）模型。我们提出了一种新颖的框架，即 NAT 建模 BN 的跨因果化，通过该框架，可以利用 NAT 模型中嵌入的因果独立性来实现更有效的推理。我们证明跨因果关系是精确的并且产生多项式空间复杂度。我们证明了基于惰性传播和和积网络的推理效率显着提高。