Experimental Design for Cost-Aware Learning of Causal Graphs

TL;DR

This paper addresses the problem of designing minimal cost interventions to learn causal graphs, proving NP-hardness, and proposing approximation algorithms for both general and sparse cases.

Contribution

It introduces the first approximation algorithms for cost-aware causal graph intervention design, including solutions for sparse graphs and interventions with vertex costs.

Findings

NP-hardness of the minimum cost intervention design problem

Greedy algorithm achieves constant factor approximation

Near-optimal intervention design for sparse graphs and interventions

Abstract

We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove that we can achieve a constant factor approximation to this problem with a greedy algorithm. We then constrain the sparsity of each intervention. We develop an algorithm that returns an intervention design that is nearly optimal in terms of size for sparse graphs with sparse interventions and we discuss how to use it when there are costs on the vertices.