Bayesian networks (BNs) encode conditional independence to avoid combinatorial explosion on the number of variables, but are subject to exponential growth of space and inference time on the number of causes per effect variable. Among space-efficient local models, we focus on the Non-Impeding Noisy-AND Tree (NIN-AND Tree or NAT) models, due to their multiple merits, and on NAT-modeled BNs, where each multi-parent variable family may be encoded as a NAT-model. Although BN inference is generally exponential on treewidth, the inference is tractable with NAT-modeled BNs of high treewidth and low density. In this work, we present the first study to learn NAT-modeled BNs from data. We apply the MDL principle to learning NAT-modeled BNs by developing a corresponding scoring function, and we couple it with heuristic structure search. We show that when data satisfy NAT causal independence, high treewidth, and low density structure, learning underlying NAT modeled BNs is feasible.

贝叶斯网络（BNs）对条件独立性进行编码，以避免变量数量的组合爆炸式增长，但是服从于空间的指数增长以及对每个影响变量的原因数量的推断时间。在空间效率高的本地模型中，由于其多重优点，我们重点关注非隐含噪声与树（NIN-AND Tree或NAT）模型，并关注NAT建模的BN，其中每个多父变量家族可能是编码为NAT模型。尽管BN推断通常在树宽上是指数级的，但使用高树宽和低密度的NAT建模BN可以轻松进行推断。在这项工作中，我们提出了第一个从数据中学习NAT建模的BN的研究。通过开发相应的评分功能，我们将MDL原理应用于学习NAT建模的BN，并将其与启发式结构搜索相结合。