Supplementary materials are available in addition to this article. It can be downloaded at
RJ-2023-053.zip
C. Avin, I. Shpitser and J. Pearl. Identifiability of path-specific effects. In Proceedings of international joint conference on artificial intelligence, pages. 357–363 2005.
A. Balke and J. Pearl. Counterfactual probabilities: Computational methods, bounds and applications. In Proceedings of the 10th conference on uncertainty in artificial intelligence, pages. 46–54 1994a.
A. Balke and J. Pearl. Probabilistic evaluation of counterfactual queries. In Proceedings of the 12th AAAI national conference on artificial intelligence, pages. 230–237 1994b.
E. Bareinboim and J. Pearl. Causal inference by surrogate experiments: \(z\)-identifiability. In Proceedings of the 28th conference on uncertainty in artificial intelligence, pages. 113–120 2012.
M. Chen, V. Chernozhukov, I. Fernandez-Val and B. Melly.
Counterfactual: Estimation and inference methods for counterfactual analysis. 2020. URL
https://CRAN.R-project.org/package=Counterfactual.
R package version 1.2.
G. Csardi and T. Nepusz. The
igraph software package for complex network research.
InterJournal, Complex Systems: 1695, 2006. URL
https://igraph.org.
J. Y. Halpern. Axiomatizing causal reasoning. In Proceedings of the 14th conference on uncertainty in artificial intelligence, pages. 202–210 1998.
P. W. Holland. Statistics and causal inference.
Journal of the American Statistical Association, 81(396): 945–960, 1986. URL
https://doi.org/10.1080/01621459.1986.10478354.
Y. Huang and M. Valtorta. Pearl’s calculus of intervention is complete. In Proceedings of the 22nd conference on uncertainty in artificial intelligence, pages. 217–224 2006. AUAI Press.
J. Karvanen. R6causal: R6 class for structural causal models. 2022. R package version 0.6.1.
Y. Kivva, E. Mokhtarian, J. Etesami and N. Kiyavash. Revisiting the general identifiability problem. In Proceedings of the 38th conference on uncertainty in artificial intelligence, pages. 1022–1030 2022. PMLR.
M. J. Kusner, J. Loftus, C. Russell and R. Silva. Counterfactual fairness. In Proceedings of the 31st international conference on neural information processing systems, pages. 4069–4079 2017.
S. Lee, J. D. Correa and E. Bareinboim. General identifiability with arbitrary surrogate experiments. In Proceedings of the 35th conference on uncertainty in artificial intelligence, pages. 389–398 2019. PMLR.
J. Pearl. Causal diagrams for empirical research.
Biometrika, 669–710, 1995. URL
https://doi.org/10.1093/biomet/82.4.669.
J. Pearl. Causality: Models, reasoning and inference. 2nd ed Cambridge University Press, 2009.
I. Shpitser and J. Pearl. Complete identification methods for the causal hierarchy. Journal of Machine Learning Research, 9(64): 1941–1979, 2008.
I. Shpitser and J. Pearl. Identification of conditional interventional distributions. In Proceedings of the 22nd conference on uncertainty in artificial intelligence, pages. 437–444 2006a. AUAI Press.
I. Shpitser and J. Pearl. Identification of joint interventional distributions in recursive semi-Markovian causal models. In Proceedings of the 21st national conference on artificial intelligence - volume 2, pages. 1219–1226 2006b. AAAI Press.
I. Shpitser and J. Pearl. What counterfactuals can be tested. In Proceedings of the 23rd conference on uncertainty in artificial intelligence, pages. 352–359 2007. AUAI Press.
H. Stoll, G. King, L. Zeng, C. Gandrud and B. Sabath.
WhatIf: Software for evaluating counterfactuals. 2020. URL
https://CRAN.R-project.org/package=WhatIf.
R package version 1.5-10.
J. Textor, B. van der Zander, M. S. Gilthorpe, M. Liśkiewicz and G. T. Ellison. Robust causal inference using directed acyclic graphs: The
R package
dagitty.
International Journal of Epidemiology, 45(6): 1887–1894, 2017. URL
https://doi.org/10.1093/ije/dyw341.
J. Tian and J. Pearl. A general identification condition for causal effects. In Proceedings of the 19th AAAI national conference on artificial intelligence, pages. 567–573 2002.
S. Tikka, A. Hyttinen and J. Karvanen. Causal effect identification from multiple incomplete data sources: A general search-based approach.
Journal of Statistical Software, 99(5): 1–40, 2021. URL
https://doi.org/10.18637/jss.v099.i05.
S. Tikka and J. Karvanen. Identifying causal effects with the
R package
causaleffect.
Journal of Statistical Software, 76(12): 1–30, 2017. URL
https://doi.org/10.18637/jss.v076.i12.
S. Tikka and J. Karvanen. Surrogate outcomes and transportability. International Journal of Approximate Reasoning, 108: 21–37, 2019.
T. S. Verma and J. Pearl. Equivalence and synthesis of causal models. In Proceedings of the 6th conference on uncertainty in artificial intelligence, pages. 255–270 1990.
J. Zhang and E. Bareinboim. Fairness in decision-making — the causal explanation formula. In Proceedings of the 32nd AAAI conference on artificial intelligence, pages. 2037–2045 2018.