Abstract: Learning causal network by combining observational data and intervention data is a machine learning method based on intervention, and the intervention learning can discover causal relationships of network from small samples. The influences of disturbance for causality mainly embody in network parameters. This paper presents an interventional learning algorithm on causal network parameters based on sensitivity analysis (ILPSA). For a known prior network, ILPSA algorithm uses junction tree inference algorithm to produce the sensitivity function, and proposes the active selection method of intervention nodes by analyzing the parameter importance of sensitivity function. Further, it manipulates the intervention nodes to produce the intervention data, combines observational data and intervention data, learns the parameters of causal network by maximum likelihood estimation (MLE) method, and measures the learning results by KL divergence. The results of algorithm comparison and experiment show that ILPSA algorithm is better than the methods of random intervention and no intervention, especially, the ILPSA algorithm is more effective in the smaller samples.

Key words: sensitivity analysis, intervention learning, causal network, maximum likelihood estimation (MLE)

摘要： 联合观察数据和扰动数据学习因果网络是一种基于扰动的机器学习方法, 通过扰动学习可以利用少量样本发现网络中的因果关系, 扰动对于因果关系的影响主要体现在网络参数方面。提出了一种基于灵敏性分析的因果网络参数的扰动学习算法(intervention learning of parameter sensitivity analysis, ILPSA)。对于给定的先验网络, ILPSA算法利用联合树推理算法生成灵敏性函数, 通过对灵敏性函数的参数重要性分析提出扰动结点的一种主动选取方法; 对扰动结点的主动干扰产生扰动数据, 然后联合观察数据和扰动数据, 利用最大似然估计(maximum likelihood estimation, MLE)方法学习因果网络的参数, 并利用KL距离对学习结果进行评价。算法比较和实验结果表明, ILPSA算法的学习结果明显好于随机选择扰动结点和无扰动情况下的方法, 特别在样本较小的情况下优势更明显。

关键词: 灵敏性分析, 扰动学习, 因果网络, 最大似然估计(MLE)