Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data
arxiv(2022)
摘要
Constraint-based causal discovery methods leverage conditional independence
tests to infer causal relationships in a wide variety of applications. Just as
the majority of machine learning methods, existing work focuses on studying
independent and identically distributed data. However, it is known
that even with infinite i.i.d. data, constraint-based methods can only
identify causal structures up to broad Markov equivalence classes, posing a
fundamental limitation for causal discovery. In this work, we observe that
exchangeable data contains richer conditional independence structure than
i.i.d. data, and show how the richer structure can be leveraged for causal
discovery. We first present causal de Finetti theorems, which state that
exchangeable distributions with certain non-trivial conditional independences
can always be represented as independent causal mechanism (ICM)
generative processes. We then present our main identifiability theorem, which
shows that given data from an ICM generative process, its unique causal
structure can be identified through performing conditional independence tests.
We finally develop a causal discovery algorithm and demonstrate its
applicability to inferring causal relationships from multi-environment data.
Our code and models are publicly available at:
https://github.com/syguo96/Causal-de-Finetti
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