We study the problem of separating a mixture of distributions, all of which come from interventions on a known causal bayesian network. Given oracle access to marginals of all distributions resulting from interventions on the network, and estimates of marginals from the mixture distribution, we want to recover the mixing proportions of different mixture components. We show that in the worst case, mixing proportions cannot be identified using marginals only. If exact marginals of the mixture distribution were known, under a simple assumption of excluding a few distributions from the mixture, we show that the mixing proportions become identifiable. Our identifiability proof is constructive and gives an efficient algorithm recovering the mixing proportions exactly. When exact marginals are not available, we design an optimization framework to estimate the mixing proportions. Our problem is motivated from a real-world scenario of an e-commerce business, where multiple interventions occur at a given time, leading to deviations in expected metrics. We conduct experiments on the well known publicly available ALARM network and on a proprietary dataset from a large e-commerce company validating the performance of our method.

该研究研究了从已知的因果贝叶斯网络中进行的干预的混合分布的分离问题，提出了一种有效算法来恢复混合成分的混合比例，并基于简单假设证明了混合物精确边际已知时可排除混合中的少数分布来使混合成分混合比例可识别，进而设计了一种估计混合比例的优化框架，并在真实场景下进行了验证。

利用聚合观测数据解开因果贝叶斯网络干预混杂问题