TY - CHAP
T1 - Efficiently finding conditional instruments for causal inference
AU - Van Der Zander, Benito
AU - Textor, Johannes
AU - Liskiewicz, Maciej
N1 - Conference code: 116754
PY - 2015/7
Y1 - 2015/7
N2 - Instrumental variables (IVs) are widely used to identify causal effects. For this purpose IVs have to be exogenous, i.e., causally unrelated to all variables in the model except the explanatory variable X. It can be hard to find such variables. A generalized IV method has been proposed that only requires exogeneity conditional on a set of covariates. This leads to a wider choice of potential IVs, but is rarely used yet. Here we address two issues with conditional IVs. First, they are conceptually rather distant to standard IVs; even variables that are independent of X could qualify as conditional IVs. We propose a new concept called ancestral IV, which interpolates between the two existing notions. Second, so far only exponential-time algorithms are known to find conditional IVs in a given causal diagram. Indeed, we prove that this problem is NP-hard. Nevertheless, we show that whenever a conditional IV exists, so does an ancestral IV, and ancestral IVs can be found in polynomial time. Together this implies a complete and constructive solution to causal effect identification using IVs in linear causal models.
AB - Instrumental variables (IVs) are widely used to identify causal effects. For this purpose IVs have to be exogenous, i.e., causally unrelated to all variables in the model except the explanatory variable X. It can be hard to find such variables. A generalized IV method has been proposed that only requires exogeneity conditional on a set of covariates. This leads to a wider choice of potential IVs, but is rarely used yet. Here we address two issues with conditional IVs. First, they are conceptually rather distant to standard IVs; even variables that are independent of X could qualify as conditional IVs. We propose a new concept called ancestral IV, which interpolates between the two existing notions. Second, so far only exponential-time algorithms are known to find conditional IVs in a given causal diagram. Indeed, we prove that this problem is NP-hard. Nevertheless, we show that whenever a conditional IV exists, so does an ancestral IV, and ancestral IVs can be found in polynomial time. Together this implies a complete and constructive solution to causal effect identification using IVs in linear causal models.
M3 - Chapter
SN - 9781577357384
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 3243
EP - 3249
BT - Proceedings of the 24th International Joint Conference on Artificial Intelligence
PB - AAAI Press
T2 - 24th International Joint Conference on Artificial Intelligence
Y2 - 25 July 2015 through 31 July 2015
ER -
SDG 9 – Industrie, Innovation und Infrastruktur