Experimental Design for Causal Effect Identification

TL;DR

This paper addresses the challenge of designing cost-effective intervention strategies to identify causal effects, proposing algorithms with theoretical guarantees and heuristics, validated through simulations.

Contribution

It formulates the intervention design problem as NP-hard, establishes a connection to the minimum hitting set problem, and introduces algorithms with approximation guarantees and heuristics.

Findings

The intervention design problem is NP-hard.

Proposed algorithms can find optimal or near-optimal solutions.

Heuristic algorithms perform well in simulations with small regret.

Abstract

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.