On the Testable Implications of Causal Models with Hidden Variables

By Jin Tian, Judea Pearl. 2002

192 citations recorded by the source corpus.

The validity of a causal model can be tested only if the model imposes constraints on the probability distribution that governs the generated data. In the presence of unmeasured variables, causal models may impose two types of constraints: conditional independencies, as read through the d-separation criterion, and functional constraints, for which no general criterion is available. This paper offers a systematic way of identifying functional constraints and, thus, facilitates the task of testing causal models as well as inferring such models from data.

Subfields: Artificial Intelligence

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Citations in the corpus

Fair Inference on Outcomes (2017, methodology): “A general characterization of identiﬁable functionals of causal effects exists (Tian and Pearl 2002; Shpitser and Pearl 2008).”
Missing Data as a Causal and Probabilistic Problem (2015, methodology): “In fact, the relationship between our algorithm and MAR is not unlike the relationship between the ID algorithm for identification of causal effects [22, 18, 19], and the conditional ignorability assumption in causal inference [13].”
Causal Graphical Models with Latent Variables: Learning and Inference (2007, methodology): “Furthermore, we believe that applying the orientation and tail augmentation rules of Zhang and Spirtes (2005a) after each experiment, might help to reduce the number of experiments needed to fully orient the structure.”
A Theoretical Study of Y Structures for Causal Discovery (2006, background): “Finally, hidden variable models are known to entail non-conditional independence constraints upon the marginal distribution; these constraints can be used to guide searches for hidden variable models that entail the constraints (Spirtes et al., 1993; Tian & Pearl, 2002).”
Recovering Causal Effects from Selection Bias (2015, methodology): “The following lemma is from (Tian and Pearl 2002b): Lemma 2 Let H ⊆ V, and assume that H is partitioned into c-components H1, .”
Pearl's Calculus of Intervention Is Complete (2006, background): “For convenience and for uniformity with [Tian and Pearl, 2002b], we deﬁne and interpret this equation as stating that Q [ S ] is the causal effect of N \ S on S .”
On the Identification of Causal Effects (2015, methodology): “A procedure that systematically finds functional constraints imposed on the observed distributions in causal models with unobserved variables is given in [Tian and Pearl, 2002b].”
CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS (2014, background): “A complete theory for identifying Y(a) from p(V), where A and Y are disjoint, was given in [25, 33].”
Graphical methods for inequality constraints in marginalized DAGs (2012, background): “Verma constraints are still poorly understood; see [10] for methods on deriving them.”
Nested Markov Properties for Acyclic Directed Mixed Graphs (2012, methodology): “The final recursive call is outlined in the third paragraph of the description of (A2) in (Tian and Pearl, 2002b), and corresponds to line 12 of Algorithm 2.”
On Pearl’s Hierarchy and the Foundations of Causal Inference (2022, methodology): “To witness, consider We introduce below a construct called confounded component [Tian and Pearl 2002b] to restore and help to make sense of modularity in these models.”