Identification of Conditional Interventional Distributions

By Ilya Shpitser, Judea Pearl. 2006

234 citations recorded by the source corpus.

The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting distributions on post-action outcomes given a set of measurements. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem, and show applications to sequential decision making.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Algorithmic recourse under imperfect causal knowledge: a probabilistic approach (2020, background): “Moreover, if only a partial graph is available or some relations are known to be confounded, one will need to restrict recourse actions to the subset of interventions that are still identiﬁable [36, 37, 41].”
Causal inference in statistics: An overview (2009, background): “More recent results extend this theorem by (1) presenting a necessary and sufficient condition for identification (Shpitser and Pearl, 2006), and (2) extending 10Before applying this criterion, one may delete from the causal graph all nodes that are not ancestors of Y . the condition from causal…”
Statistical Causality from a Decision-Theoretic Perspective (2014, background): “Statistical Causality 43 constructively (Shpitser and Pearl 2006a; Shpitser and Pearl 2006b; Huang and Valtorta 2006) that, whenever there exists a reduction of a causal expression to purely observational terms, it can be found by applying the do-calculus.”
Preventing Failures Due to Dataset Shift: Learning Predictive Models That Transport (2018, methodology): “In Shpitser and Pearl (2006a), the ID algorithm was extended to answer conditional effect queries of the 3Similarly, GX will denote a mutilated graph in which edges out of X are removed.”
Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview (2010, background): “In recent years the Artiﬁcial Intelligence community has devoted some eﬀort to ﬁnding necessary as well as suﬃcient conditions for the identiﬁability of consequences of interventions (Huang and Valtorta, 2006; Shpitser and Pearl, 2006a,b).”
A General Algorithm for Deciding Transportability of Experimental Results (2013, methodology): “It was shown elsewhere [69] that the steps of sID but line 10 correspond to sequences of standard probability manipulations and applications of the rules of do -calculus.”
Causal inference and the data-fusion problem (2016, background): “These results were developed in several stages over the past 20 years (13, 15, 17, 23, 25).”
Effects of Treatment on the Treated: Identification and Generalization (2009, methodology): “If W has a backdoor path to Y in Gx, then P (y|w, do(x)) is identifiable if and only if P (y, w|do(x)) is identifiable [8].”
Counterfactual analyses with graphical models based on local independence (2011, background): “It was shown in [12, 27] and [10] that this strategy gives a complete theory in the simpler setting of finite state or Gaussian–Bayesian networks.”
Transportability of Causal and Statistical Relations: A Formal Approach (2011, background): “Moreover, since do-calculus is complete [10], every valid equality can be obtained by a finite application of the three rules of the calculus.”
Do-calculus when the True Graph Is Unknown (2015, methodology): “…(1993, p. 79 An algorithm to apply the do -calculus when the true graph is known was developed by Tian and Pearl (2002), which with some modiﬁcations was shown to be complete for the identiﬁcation of (conditional) causal effects by Shpitser and Pearl (2006b) (see also Huang and Valtorta (2006)).”
Causal Graphical Models with Latent Variables: Learning and Inference (2007, methodology): “In order to learn graphical models with latent variables from observational data a constraint based learning algorithm has been developed by Spirtes et al. (1999). It is called the Fast Causal Inference (FCI) algorithm and it uses conditional independence relations found between observable variables”
Causal and Counterfactual Inference (2018, background): “The results stated in Theorem 1 were developed in several stages over the past 20 years (Pearl, 1993, 1995; Shpitser & Pearl, 2006; Tian & Pearl, 2002).”