Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning. (arXiv:2105.14024v1 [cs.LG])

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 experiments that 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 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



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