Optimal Experiment Design for Causal Discovery from Fixed Number of Experiments
This work addresses the challenge of causal discovery under experimental constraints, offering a practical solution for researchers in fields like biology or social sciences, though it is incremental as it builds on existing causal learning frameworks.
The paper tackles the problem of learning causal structures from a fixed number of non-adaptive experiments, proposing an algorithm that efficiently designs experiments to minimize unknown portions of the structure. It shows that for bounded degree graphs, the algorithm achieves a ρ-approximation independent of graph order, with simulations indicating performance close to optimal.
We study the problem of causal structure learning over a set of random variables when the experimenter is allowed to perform at most $M$ experiments in a non-adaptive manner. We consider the optimal learning strategy in terms of minimizing the portions of the structure that remains unknown given the limited number of experiments in both Bayesian and minimax setting. We characterize the theoretical optimal solution and propose an algorithm, which designs the experiments efficiently in terms of time complexity. We show that for bounded degree graphs, in the minimax case and in the Bayesian case with uniform priors, our proposed algorithm is a $ρ$-approximation algorithm, where $ρ$ is independent of the order of the underlying graph. Simulations on both synthetic and real data show that the performance of our algorithm is very close to the optimal solution.