Primary Submission Category: Causal Discovery
Differentiable Covariate Selection for Backdoor Adjustment
Authors: Elijah Tamarchenko, Rohit Bhattacharya,
Presenting Author: Elijah Tamarchenko*
Covariate selection for backdoor adjustment is often made difficult due to unmeasured confounding; some adjustment sets can lead to bias due to exclusion of relevant confounders, others may be unbiased but statistically inefficient. Rotnitzky et al (2019) propose a graphical criterion for identifying the optimal adjustment set – an unbiased set with minimal asymptotic variance – in settings where the structure of the causal system is known exactly and there are no unobserved common causes. However, in most practical settings, the full causal structure is unknown and likely to exhibit unmeasured confounding. In this case, Entner et al (2013) propose a procedure for identifying an unbiased adjustment set. However, it performs an exponential number of conditional independence tests, which is infeasible in high dimensional settings, and does not consider minimizing variance. We propose a parametric continuous optimization procedure, which performs both covariate selection and effect estimation in a single step. We prove that this procedure identifies the optimal adjustment set in the absence of unmeasured confounders. We further show that under mild assumptions involving an auxiliary variable, if the continuous optimization procedure excludes this variable from the covariate selection process, then the effect estimate is provably unbiased even in settings with unmeasured confounders. Further, the procedure often leads to a practical reduction in variance as shown via simulations.