A note on efficient minimum cost adjustment sets in causal graphical models

Abstract We study the selection of adjustment sets for estimating interventional mean under an individualized treatment rule. assume a non-parametric causal graphical model with, possibly, hidden variables and at least one set composed observable variables. Moreover, we that have positive costs associated with them. define cost as sum comprise it. show in this setting there exist are minimum optimal, sense they yield estimators smallest asymptotic variance among those control cost. Our results based on construction special flow network original graph. optimal can be found by computing maximum network, then finding vertices reachable from source augmenting paths. The optimaladj Python package implements algorithms introduced article.