Learning Adjustment Sets from Observational and Limited Experimental Data

Estimating causal effects from observational data is not always possible due\nto confounding. Identifying a set of appropriate covariates (adjustment set)\nand adjusting for their influence can remove confounding bias; however, such a\nset is typically not identifiable from observational data alone. Experimental\ndata do not have confounding bias, but are typically limited in sample size and\ncan therefore yield imprecise estimates. Furthermore, experimental data often\ninclude a limited set of covariates, and therefore provide limited insight into\nthe causal structure of the underlying system. In this work we introduce a\nmethod that combines large observational and limited experimental data to\nidentify adjustment sets and improve the estimation of causal effects. The\nmethod identifies an adjustment set (if possible) by calculating the marginal\nlikelihood for the experimental data given observationally-derived prior\nprobabilities of potential adjustmen sets. In this way, the method can make\ninferences that are not possible using only the conditional dependencies and\nindependencies in all the observational and experimental data. We show that the\nmethod successfully identifies adjustment sets and improves causal effect\nestimation in simulated data, and it can sometimes make additional inferences\nwhen compared to state-of-the-art methods for combining experimental and\nobservational data.\n