We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log 2 (N ) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 < K < 1 2 N we provide an upper bound on the number experiments required to determine causal structure when each experiment simultaneously randomizes K variables. For large N , these bounds are significantly lower than the N − 1 bound required when each experiment randomizes at most one variable. For k max < N 2 , we show that ( N kmax −1)+ N 2kmax log 2 (k max ) experiments are sufficient and in the worst case necessary. We offer a conjecture as to the minimal number of experiments that are in the worst case sufficient to identify all causal relations among N observed variables that are a subset of the vertices of a DAG.
REF introduced the constraint on the number of variables intervened in each experiment.
On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations Among N Variables
ArXiv
ArXiv
Computer Science Mathematics