Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.

翻译：珍珠的计算法是一种完全不言而喻的方法, 来了解观察数据的可识别因果效应。 当这种效果无法识别时, 必须在系统中进行一系列往往昂贵的干预, 以了解因果关系。 在这项工作中, 我们考虑设计干预措施的收集问题, 以最低成本来辨别预期效果。 首先, 我们证明这个问题是难以解决的, 并随后提出一种算法, 它可以找到最佳的解决方案或对数因素近似。 这是通过在我们的问题和最小撞击设定的问题之间建立联系来完成的。 此外, 我们建议采用几种多元时超常算法来解决这个问题的计算复杂性。 虽然这些算法可能会在亚最佳解决方案上出现意外, 但我们的模拟显示, 它们在随机图表上取得了很小的遗憾。