N-1 Experiments Suffice to Determine the Causal Relations Among N Variables

  

Clark Glymour

Institute for Human and Machine Cognition

 

By combining experimental interventions with search procedures for graphical causal models we show that under familiar assumptions, with perfect data, N- 1 experiments suffice to determine the causal relations among N>2 variables when each experiment randomizes at most one variable. We show the same bound holds for adaptive learners, but does not hold for N > 4 when each experiment can simultaneously randomize more than one variable. This bound provides a type of ideal for the measure of success of heuristic approaches in active learning methods of causal discovery, which currently use less informative measures.