Experimental Design for Causal Effect Identification
This work addresses the challenge of efficiently designing interventions for causal inference, which is crucial for fields like epidemiology and economics, though it is incremental as it builds on existing causal identification frameworks.
The paper tackles the problem of designing a minimum-cost set of interventions to identify a causal effect when it is not identifiable from observational data alone, proving the problem is NP-hard and providing an algorithm that finds either the optimal solution or a logarithmic-factor approximation, with simulations showing small regrets on random graphs.
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.