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Abstract
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 exponentialtime algorithms are known to find conditional IVs in a given causal diagram. Indeed, we prove that this problem is NPhard. 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.
Original language  English 

Title of host publication  Proceedings of the 24th International Joint Conference on Artificial Intelligence 
Number of pages  7 
Publisher  AAAI Press 
Publication date  07.2015 
Pages  32433249 
ISBN (Print)  9781577357384 
Publication status  Published  07.2015 
Event  24th International Joint Conference on Artificial Intelligence  Buenos Aires, Argentina Duration: 25.07.2015 → 31.07.2015 Conference number: 116754 http://ijcai15.org/ 
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 1 Finished

Causality: an algorithmic framework and a computational complexity perspective
Liskiewicz, M. & Textor, J.
01.01.16 → 31.12.22
Project: DFG Projects › DFG Individual Projects