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.

本研究主要在于探究具有潜在共变量和环路的结构因果模型，并证明其遵守特定可解性条件下的便利性质，这一工作将结构因果模型在具有周期的情况下进行了推广，从而提供了一般性的统计因果建模的基础。