论文标题
从不完整的数据中学习贝叶斯网络的可能性
Learning Bayesian Networks from Incomplete Data with the Node-Average Likelihood
论文作者
论文摘要
从完整数据中学习的贝叶斯网络（BN）结构在文献中进行了广泛的研究。但是，对于不完整的数据，理论结果较少，并且大多数与期望最大化（EM）算法有关。 Balov（2013）提出了一种称为节点平均可能性（NAL）的替代方法，该方法与EM具有竞争力，但在计算上更有效。他证明了其对离散BN的一致性和模型可识别性。 在本文中，我们为NAL的一致性提供了足够的条件。我们证明了有条件的高斯BN的一致性和可识别性，其中包括离散和高斯BN作为特殊情况。此外，我们通过独立的模拟研究确认了我们的结果和Balov（2013）的结果。因此，我们证明了NAL的适用性比Balov（2013）最初暗示的要宽得多，并且它与EM竞争也是有条件的高斯BN。
Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are related to the Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative approach called Node-Average Likelihood (NAL) that is competitive with EM but computationally more efficient; and he proved its consistency and model identifiability for discrete BNs. In this paper, we give general sufficient conditions for the consistency of NAL; and we prove consistency and identifiability for conditional Gaussian BNs, which include discrete and Gaussian BNs as special cases. Furthermore, we confirm our results and the results in Balov (2013) with an independent simulation study. Hence we show that NAL has a much wider applicability than originally implied in Balov (2013), and that it is competitive with EM for conditional Gaussian BNs as well.
