Optimal Experiment Design for Causal Discovery from Fixed Number of Experiments

TL;DR

This paper addresses optimal experimental design for causal discovery with a limited number of non-adaptive experiments, providing theoretical solutions and an efficient algorithm that performs near-optimally in various settings.

Contribution

It characterizes the optimal strategy for causal structure learning with limited experiments and introduces a time-efficient algorithm with provable approximation guarantees.

Findings

Algorithm achieves near-optimal performance on synthetic data.

Proven approximation ratio independent of graph size.

Effective in both Bayesian and minimax scenarios.

Abstract

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 $\rho$-approximation algorithm, where $\rho$ 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.