- J. Aldrich. 1989. Autonomy. Oxford Econ. Pap. 41, 15–34. DOI: .Google ScholarCross Ref
- E. Bareinboim and J. Pearl. 2012. Causal inference by surrogate experiments: z-Identifiability. In N. d. F. Murphy and Kevin (Eds.), Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 113–120.Google Scholar
- E. Bareinboim and J. Pearl. 2016. Causal inference and the data-fusion problem. Proc. Natl. Acad. Sci. 113, 27, 7345–7352. DOI: .Google ScholarCross Ref
- E. Bareinboim, C. Brito, and J. Pearl. 2012. Local characterizations of causal Bayesian networks. In M. Croitoru, S. Rudolph, N. Wilson, J. Howse, and O. Corby (Eds.), Graph Structures for Knowledge Representation and Reasoning. Springer Berlin Heidelberg, Berlin, Heidelberg, 1–17. DOI: .Google ScholarDigital Library
- E. Bareinboim, J. D. Correa, D. Ibeling, and T. Icard. 2020. On Pearl’s Hierarchy and the Foundations of Causal Inference. Technical Report R-60, Causal AI Lab, Columbia University.Google Scholar
- E. W. Beth. 1956. On Padoa’s method in the theory of definition. J. Symb. Log. 2, 1, 194–195. DOI: .Google ScholarCross Ref
- R. Briggs. 2012. Interventionist counterfactuals. Philos. Stud. 160, 1, 139–166. DOI: .Google ScholarCross Ref
- N. Cartwright. 1989. Nature’s Capacities and Their Measurement. Clarendon Press, Oxford. DOI: .Google ScholarCross Ref
- N. Chomsky. 1959. On certain formal properties of grammars. Inf. Control. 2, 137–167. .Google ScholarCross Ref
- A. P. Dawid. 2000. Causal inference without counterfactuals (with comments and rejoinder). J. Am. Stat. Assoc. 95, 450, 407–448. DOI: .Google ScholarCross Ref
- R. Fagin, J. Y. Halpern, and N. Megiddo. 1990. A logic for reasoning about probabilities. Inf. Comput. 87, 1/2, 78–128. DOI: .Google ScholarDigital Library
- R. A. Fisher. 1936. Design of experiments. Br. Med. J. 1, 3923, 554. DOI: .Google ScholarCross Ref
- D. Galles and J. Pearl. 1995. Testing identifiability of causal effects. In P. Besnard and S. Hanks (Eds.), Uncertainty in Artificial Intelligence 11. Morgan Kaufmann, San Francisco, 185–195.Google Scholar
- D. Galles and J. Pearl. 1998. An axiomatic characterization of causal counterfactuals. Found. Sci. 3, 1, 151–182. DOI: .Google ScholarCross Ref
- T. Haavelmo. 1943. The statistical implications of a system of simultaneous equations. Econometrica 11, 1, 1. DOI: .Google ScholarCross Ref
- J. Y. Halpern. 1998. Axiomatizing causal reasoning. In G. F. Cooper and S. Moral (Eds.), Uncertainty in Artificial Intelligence. Cornell University, Morgan Kaufmann, San Francisco, CA, 202–210.Google Scholar
- J. Y. Halpern. 2000. Axiomatizing causal reasoning. J. Artif. Intell. Res. 12, 317–337. DOI: .Google ScholarCross Ref
- J. Y. Halpern. 2013. From causal models to counterfactual structures. Rev. Symb. Logic. 6, 2, 305–322. DOI: .Google ScholarCross Ref
- Y. Huang and M. Valtorta. 2006. Identifiability in causal Bayesian networks: A sound and complete algorithm. In Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI 2006). AAAI Press, Menlo Park, CA, 1149–1156.Google Scholar
- D. Hume. 1739. A Treatise of Human Nature. Oxford University Press, Oxford.Google Scholar
- D. Hume. 1748. An Enquiry Concerning Human Understanding. Open Court Press, LaSalle.Google Scholar
- D. Ibeling and T. Icard. 2018. On the conditional logic of simulation models. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI-18. 1868–1874. DOI: .Google ScholarCross Ref
- D. Ibeling and T. Icard. 2019. On open-universe causal reasoning. In Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence.Google Scholar
- D. Ibeling and T. Icard. 2020. Probabilistic reasoning across the causal hierarchy. In Proceedings of the 34th AAAI Conference on Artificial Intelligence. DOI: .Google ScholarCross Ref
- T. Icard. 2020. Calibrating generative models: The probabilistic Chomsky–Schützenberger hierarchy. J. Math. Psychol. 95. DOI: .Google ScholarCross Ref
- G. W. Imbens and D. B. Rubin. 2015. Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press, Cambridge, MA. DOI: .Google ScholarCross Ref
- D. Koller and N. Friedman. 2009. Probabilistic Graphical Models: Principles and Techniques. MIT Press.Google Scholar
- M. Kuroki and M. Miyakawa. 1999. Identifiability criteria for causal effects of joint interventions. J. R. Stat. Soc. 29, 105–117. DOI: .Google ScholarCross Ref
- S. L. Lauritzen. 1996. Graphical Models. Clarendon Press, Oxford.Google Scholar
- S. Lee, J. D. Correa, and E. Bareinboim. 2019. General identifiability with arbitrary surrogate experiments. In Proceedings of the Thirty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence. AUAI Press, in press, Corvallis, OR.Google Scholar
- D. Lewis. 1973. Counterfactuals. Harvard University Press, Cambridge, MA.Google Scholar
- J. Locke. 1690. An Essay Concerning Human Understanding. London, Thomas Basset.Google Scholar
- J. L. Mackie. 1980. The Cement of the Universe: A Study of Causation. Clarendon Press, Oxford. DOI: .Google ScholarCross Ref
- J. Marschak. 1950. Statistical inference in economics. In T. Koopmans (Ed.), Statistical Inference in Dynamic Economic Models. Wiley, New York, 1–50.Google Scholar
- T. Maudlin. 2019. The why of the world. Boston Review. https://bostonreview.net/science-nature/tim-maudlin-why-world. Accessed Febuary 10, 2020.Google Scholar
- J. Neyman. 1923. On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Stat. Sci. 5, 4, 465–480. DOI: .Google ScholarCross Ref
- J. Pearl. 1988. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo, CA.Google ScholarDigital Library
- J. Pearl. 1993. Aspects of graphical models connected with causality. In Proceedings of the 49th Session of the International Statistical Institute, 1 (August), 399–401.Google Scholar
- J. Pearl. 1995. Causal diagrams for empirical research. Biometrika 82, 4, 669–688. DOI: .Google ScholarCross Ref
- J. Pearl. 2000. Causality: Models, Reasoning, and Inference. (2nd. ed.). Cambridge University Press, NY. DOI: .Google ScholarCross Ref
- J. Pearl. 2001. Bayesianism and causality, or, why I am only a half-Bayesian. In Foundations of Bayesianism, Applied Logic Series, Volume 24. Kluwer Academic Publishers, 19–36. DOI: .Google ScholarCross Ref
- J. Pearl. 2012. The mediation formula: A guide to the assessment of causal pathways in nonlinear models. In C. Berzuini, P. Dawid, and L. Bernardinelli (Eds.), Causality: Statistical Perspectives and Applications, John Wiley and Sons, Ltd, Chichester, UK, 151–179. DOI: .Google ScholarCross Ref
- J. Pearl and E. Bareinboim. 2019. A note on “generalizability of study results.” J. Epidemiol. 30, 186–188. DOI: .Google ScholarCross Ref
- J. Pearl and D. Mackenzie. 2018. The Book of Why. Basic Books, New York.Google Scholar
- J. Pearl and J. M. Robins. 1995. Probabilistic evaluation of sequential plans from causal models with hidden variables. In Uncertainty in Artificial Intelligence 11. Morgan Kaufmann, 444–453.Google Scholar
- D. C. Penn and D. J. Povinelli. 2007. Causal cognition in human and nonhuman animals: A comparative, critical review. Annu. Rev. Psychol. 58, 97–118. DOI: .Google ScholarCross Ref
- J. Peters, D. Janzing, and B. Schlkopf. 2017. Elements of Causal Inference: Foundations and Learning Algorithms. The MIT Press.Google Scholar
- G. de Pierris. 2015. Ideas, Evidence, and Method: Hume’s Skepticism and Naturalism concerning Knowledge and Causation. Oxford University Press. DOI: .Google ScholarCross Ref
- J. M. Robins. 1986. A new approach to causal inference in mortality studies with a sustained exposure period—applications to control of the healthy workers survivor effect. Math. Model. 7, 1393–1512. DOI: .Google ScholarCross Ref
- P. R. Rosenbaum and D. B. Rubin. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 1, 41–55. DOI: .Google ScholarCross Ref
- P. K. Rubenstein, S. Weichwald, S. Bongers, J. M. Mooij, D. Janzing, M. Grosse-Wentrup, and B. Schölkopf. 2017. Causal consistency of structural equation models. In Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence (UAI).Google Scholar
- D. B. Rubin. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol. 66, 5, 688–701. DOI: .Google ScholarCross Ref
- B. Schölkopf. 2019. Causality for machine learning. arXiv preprint arXiv:1911.10500.Google Scholar
- I. Shpitser and J. Pearl. 2006. Identification of joint interventional distributions in recursive semi-Markovian causal models. In Proceedings of the Twenty-First AAAI Conference on Artificial Intelligence. 2, 1219–1226.Google Scholar
- H. A. Simon. 1953. Causal ordering and identifiability. In W. C. Hood and T. C. Koopmans (Eds.), Studies in Econometric Method, Wiley and Sons, Inc., New York, 49–74. DOI: .Google ScholarCross Ref
- P. Spirtes, C. N. Glymour, and R. Scheines. 2001. Causation, Prediction, and Search. (2nd. ed.). MIT Press.Google Scholar
- L. J. Stockmeyer. 1977. The polynomial-time hierarchy. Theor. Comput. Sci. 3, 1–22. DOI: .Google ScholarCross Ref
- R. H. Strotz and H. O. A. Wold. 1960. Recursive versus nonrecursive systems: An attempt at synthesis. Econometrica 28, 417–427. DOI: .Google ScholarCross Ref
- P. Suppes and M. Zanotti. 1981. When are probabilistic explanations possible? Synthese 48, 191–199. DOI: .Google ScholarCross Ref
- R. S. Sutton and A. G. Barto. 2018. Reinforcement Learning: An Introduction. (2nd. ed.) The MIT Press.Google Scholar
- J. Tian and J. Pearl. 2002a. A general identification condition for causal effects. In Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI 2002). 567–573.Google ScholarDigital Library
- J. Tian and J. Pearl. 2002b. On the testable implications of causal models with hidden variables. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence. 519–527.Google Scholar
- T. VanderWeele. 2015. Explanation in Causal Inference: Methods for Mediation and Interaction. Oxford University Press.Google Scholar
- J. Woodward. 2003. Making Things Happen. Oxford University Press, New York. DOI: .Google ScholarCross Ref
- G. H. von Wright. 1971. Explanation and Understanding. Cornell University Press. DOI: .Google ScholarCross Ref
- J. Zhang. 2013. A Lewisian logic of causal counterfactuals. Minds Mach. 23, 77–93. DOI: .Google ScholarDigital Library
- J. Zhang and E. Bareinboim. 2018. Fairness in decision-making—the causal explanation formula. In Proceedings of the 32nd AAAI Conference on Artificial Intelligence. 2037–2045.Google Scholar
Index Terms
- On Pearl’s Hierarchy and the Foundations of Causal Inference
Recommendations
Linking granger causality and the pearl causal model with settable systems
NIPSMINI'09: Proceedings of the 12th International Conference on Neural Information Processing Systems (NIPS)Mini-Symposium on Causality in Time SeriesThe causal notions embodied in the concept of Granger causality have been argued to belong to a different category than those of Judea Pearl's Causal Model, and so far their relation has remained obscure. Here, we demonstrate that these concepts are in ...
Causal inference and causal explanation with background knowledge
UAI'95: Proceedings of the Eleventh conference on Uncertainty in artificial intelligenceThis paper presents correct algorithms for answering the following two questions; (i) Does there exist a causal explanation consistent with a set of background knowledge which explains all of the observed independence facts in a sample? (ii) Given that ...
Inference in multi-agent causal models
In this article, we demonstrate the usefulness of causal Bayesian networks as probabilistic reasoning systems. The biggest advantage of causal Bayesian networks over traditional probabilistic Bayesian networks is that they sometimes allow to perform ...
Comments