On Searching for Generalized Instrumental Variables

@InProceedings{pmlr-v51-vanderzander16,
  title = 	 {On Searching for Generalized Instrumental Variables},
  author = 	 {Zander, Benito and Liśkiewicz, Maciej},
  booktitle = 	 {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1214--1222},
  year = 	 {2016},
  editor = 	 {Gretton, Arthur and Robert, Christian C.},
  volume = 	 {51},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Cadiz, Spain},
  month = 	 {09--11 May},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v51/vanderzander16.pdf},
  url = 	 {https://proceedings.mlr.press/v51/vanderzander16.html},
  abstract = 	 {Instrumental Variables  are a popular way to identify the direct causal effect of a random variable X on a variable Y.  Often no single instrumental variable exists, although it is still possible to find a set of generalized instrumental variables (GIVs) and identify the causal effect of all these variables at once.  Till now it was not known how to find GIVs systematically or even test efficiently, if given variables satisfy GIV conditions.  We provide fast algorithms for searching and testing restricted cases of GIVs.  However, we prove that in the most general case it is NP-hard to verify if given variables fulfill the conditions of a general instrumental sets.}
}