Foundations of structural causal models with cycles and latent variables
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Foundations of structural causal models with cycles and latent variables. / Bongers, Stephan; Forré, Patrick; Peters, Jonas; Mooij, Joris M.
In: Annals of Statistics, Vol. 49, No. 5, 2021, p. 2885-2915.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Foundations of structural causal models with cycles and latent variables
AU - Bongers, Stephan
AU - Forré, Patrick
AU - Peters, Jonas
AU - Mooij, Joris M.
N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2021.
PY - 2021
Y1 - 2021
N2 - Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do not always induce unique observational, interventional and counterfactual distributions; a marginalization does not always exist, and if it exists the marginal model does not always respect the latent projection; they do not always satisfy a Markov property; and their graphs are not always consistent with their causal semantics. We prove that for SCMs in general each of these properties does hold under certain solvability conditions. Our work generalizes results for SCMs with cycles that were only known for certain special cases so far. We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs. With this paper, we aim to provide the foundations for a general theory of statistical causal modeling with SCMs.
AB - Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do not always induce unique observational, interventional and counterfactual distributions; a marginalization does not always exist, and if it exists the marginal model does not always respect the latent projection; they do not always satisfy a Markov property; and their graphs are not always consistent with their causal semantics. We prove that for SCMs in general each of these properties does hold under certain solvability conditions. Our work generalizes results for SCMs with cycles that were only known for certain special cases so far. We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs. With this paper, we aim to provide the foundations for a general theory of statistical causal modeling with SCMs.
KW - Causal graph
KW - Counterfactuals
KW - Cycles
KW - Interventions
KW - Marginalization
KW - Markov properties
KW - Solvability
KW - Structural causal models
U2 - 10.1214/21-AOS2064
DO - 10.1214/21-AOS2064
M3 - Journal article
AN - SCOPUS:85120088356
VL - 49
SP - 2885
EP - 2915
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 5
ER -
ID: 289459995