Sample Efficient Bayesian Learning of Causal Graphs from Interventions
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利用干预样本高效开展因果图的贝叶斯学习
- 研究问题
- 当干预样本数量有限且获取成本较高时，如何结合观测信息与干预设计学习因果图，并回答特定因果效应问题？
- 方法与思路
- 作者利用均匀 DAG 抽样枚举目标集的切割配置和干预分布，更新后验，并随机干预覆盖全部边的目标顶点集合。
- 材料陈述的贡献
- 摘要称，样本足够多时算法以高概率恢复真实图，模拟中的结构汉明距离优于比较基准，并展示不可干预变量的效应估计。
- 阅读关注点
- 应核对起始图信息、干预机制与目标集选择，以及恢复保证的样本需求、后验计算成本和效应估计示例的条件。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未给出高概率保证的假设、样本界或比较数值。
原文摘要
Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence class, necessitating interventional data to learn the complete causal graph. Most works in the literature design causal discovery policies with perfect interventions, i.e., they have access to infinite interventional samples. This study considers a Bayesian approach for learning causal graphs with limited interventional samples, mirroring real-world scenarios where such samples are usually costly to obtain. By leveraging the recent result of Wienöbst et al. (2023) on uniform DAG sampling in polynomial time, we can efficiently enumerate all the cut configurations and their corresponding interventional distributions of a target set, and further track their posteriors. Given any number of interventional samples, our proposed algorithm randomly intervenes on a set of target vertices that cut all the edges in the graph and returns a causal graph according to the posterior of each target set. When the number of interventional samples is large enough, we show theoretically that our proposed algorithm will return the true causal graph with high probability. We compare our algorithm against various baseline methods on simulated datasets, demonstrating its superior accuracy measured by the structural Hamming distance between the learned DAG and the ground truth. Additionally, we present a case study showing how this algorithm could be modified to answer more general causal questions without learning the whole graph. As an example, we illustrate that our method can be used to estimate the causal effect of a variable that cannot be intervened.