Pearl's Calculus of Intervention Is Complete

By Yimin Huang, Marco G. Valtorta. 2006

254 citations recorded by the source corpus.

This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal relationships. We first review Pearl's work on this topic [Pearl, 1995], in which several useful graphical criteria are presented. Then we present a complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem. By exploiting the completeness of this algorithm, we prove that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

External Validity: From Do-Calculus to Transportability Across Populations (2014, methodology): “Q = P(y|do(x), z) (Shpitser and Pearl, 2006; Huang and Valtorta, 2006), which means that if Q cannot be expressed in terms of the probability of observables P by repeated application of these three rules, such an expression does not exist.”
Causal inference and the data-fusion problem (2016, background): “The do-calculus was proved to be complete for queries in the formQ=PðyjdoðxÞ, zÞ (14, 15), which A B C”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, methodology): “The ID algorithm, introduced by Tian and Pearl (2002) solves the identification problem; the algorithm, which applies to ADMGs, was proved to be complete by Shpitser and Pearl (2006) and also independently by Huang and Valtorta (2006).”
Causal and Counterfactual Inference (2018, background): “The do-calculus was proven to be complete for queries in the form Q = P (y|do(x), z) Huang and Valtorta (2006); Shpitser and Pearl (2006), which means that if Q cannot be reduced to probabilities of observables by repeated application of these three rules, such a reduction does not exist, i.”
Generalized Adjustment Under Confounding and Selection Biases (2018, unknown): “The do-calculus was shown complete for non-parametric identifiability (Tian and Pearl 2002; Huang and Valtorta 2006; Shpitser and Pearl 2006; Bareinboim and Pearl 2012a).”
Complete Identification Methods for the Causal Hierarchy (2008, result): “Some of the results found in this paper were also derived independently elsewhere (Huang and Valtorta, 2006b,a).”
Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality (2013, methodology): “Tian and Pearl (2002) presented an algorithm that was shown to be complete for the identification of intervention distributions; see Huang and Valtorta (2006); Shpitser and Pearl (2006b); the algorithm was extended to cover conditional intervention distributions in Shpitser and Pearl (2006a). Howeve”
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.”
On Identifying Total Effects in the Presence of Latent Variables and Selection bias (2008, methodology): “…and a response variable．Based on the theory of the identifiable factor model, we propose new graphical identifiability criteria to identify total effects under situations where it is difficult to use the identifiability criteria provided by Pearl and his colleagues and Huang and Valtorta (2006).”
Transfer Learning in Multi-Armed Bandits: A Causal Approach (2017, background): “The do-calculus was shown to be complete for identification, i.e., any causal effect can be identified from observational and experimental data if and only if it can be derived by do-calculus [Tian and Pearl, 2002; Shpitser and Pearl, 2006; Huang and Valtorta, 2006; Bareinboim and Pearl, 2012].”
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.”
Causal Graphical Models with Latent Variables: Learning and Inference (2007, unknown): “shown that do-calculus is complete (Huang and Valtorta, 2006; Shpitser and Pearl, 2006).”
Transportability across studies: A formal approach (2011, background): “(2010); Pearl (2012)), and need not enter the definition of informational surrogates. Joffe and Green (2009) compared the mediation-based and “principal surrogate” approaches to surrogacy and concluded that all approaches suffer from sensitivity to modeling assumptions, especially in the presence of”
CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS (2014, background): “ID was shown to be complete in [21, 3], in the sense that if line 5 is ever called by ID with an ADMG argument G(V, ∅), then there exists a DAG G∗ with a latent projection G(V, ∅), such that there are two members of the FFRCISTG model for G∗ that agree on p(V) but disagree on p(Y(a)).”