Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning

Abstract

Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest. We address the largely unexplored problem of designing a batch of experiments that each simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of a budget-constrained batch of experiments. By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms. Our algorithms empirically perform superior to both random interventions and algorithms that only select single-variable interventions.

arXiv comment10 pages, 2 figures, appendix, to be published in 35th Conference on Neural Information Processing Systems (NeurIPS 2021), fixed typos and clarified wording

References in corpus (9)

• Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs
• Joint Causal Inference from Multiple Contexts
• Permutation-based Causal Inference Algorithms with Interventions
• On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations Among N Variables
• Learning and Testing Causal Models with Interventions
• Stochastic Conditional Gradient++
• LazyIter: A Fast Algorithm for Counting Markov Equivalent DAGs and Designing Experiments
• Interventional Experiment Design for Causal Structure Learning
• Cost-Optimal Learning of Causal Graphs