Experimental Design for Cost-Aware Learning of Causal Graphs
This work addresses the challenge of minimizing intervention costs for causal discovery, which is incremental as it builds on existing graph learning methods.
The paper tackles the problem of designing cost-effective interventions to learn causal graphs, proving it is NP-hard and providing a greedy algorithm with constant factor approximation, along with a near-optimal algorithm for sparse graphs with sparse interventions.
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.