When does the ID algorithm fail?
Abstract: The ID algorithm solves the problem of identification of interventional distributions of the form p(Y | do(a)) in graphical causal models, and has been formulated in a number of ways [12, 9, 6]. The ID algorithm is sound (outputs the correct functional of the observed data distribution whenever p(Y | do(a)) is identified in the causal model represented by the input graph), and complete (explicitly flags as a failure any input p(Y | do(a)) whenever this distribution is not identified in the causal model represented by the input graph). The reference [9] provides a result, the so called "hedge criterion" (Corollary 3), which aims to give a graphical characterization of situations when the ID algorithm fails to identify its input in terms of a structure in the input graph called the hedge. While the ID algorithm is, indeed, a sound and complete algorithm, and the hedge structure does arise whenever the input distribution is not identified, Corollary 3 presented in [9] is incorrect as stated. In this note, I outline the modern presentation of the ID algorithm, discuss a simple counterexample to Corollary 3, and provide a number of graphical characterizations of the ID algorithm failing to identify its input distribution.
- Robin J. Evans. Margins of discrete bayesian networks. Annals of Statistics, 46:2623–2656, 2018.
- Steffen L. Lauritzen. Graphical Models. Oxford, U.K.: Clarendon, 1996.
- A potential outcomes calculus for identifying conditional path-specific effects. In Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, 2019.
- Judea Pearl. Probabilistic Reasoning in Intelligent Systems. Morgan and Kaufmann, San Mateo, 1988.
- Judea Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2 edition, 2009.
- Nested Markov properties for acyclic directed mixed graphs. Annals of Statistics, 51(1):334–361, 2023.
- James M. Robins. A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survivor effect. Mathematical Modeling, 7:1393–1512, 1986.
- Acyclic linear sems obey the nested markov property. In Proceedings of the 34th Annual Conference on Uncertainty in Artificial Intelligence (UAI-18), 2018.
- Identification of joint interventional distributions in recursive semi-Markovian causal models. In Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI-06). AAAI Press, Palo Alto, 2006.
- Multivariate counterfactual systems and causal graphical models. In Probabilistic and Causal Inference: The Works of Judea Pearl, pages 813–852, 2022.
- The proximal ID algorithm. https://arxiv.org/abs/2108.06818, 2021.
- On the testable implications of causal models with hidden variables. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI-02), volume 18, pages 519–527. AUAI Press, Corvallis, Oregon, 2002.
- Equivalence and synthesis of causal models. Technical Report R-150, Department of Computer Science, University of California, Los Angeles, 1990.
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