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#### A Weaker Faithfulness Assumption based on Triple Interactions

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arXiv:2010.14265.pdf

(Preprint), 575KB

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##### Citation

Marx, A., Gretton, A., & Mooij, J. M. (2021). A Weaker Faithfulness Assumption based on Triple Interactions. Retrieved from https://arxiv.org/abs/2010.14265.

Cite as: https://hdl.handle.net/21.11116/0000-0008-0BCE-5

##### Abstract

One of the core assumptions in causal discovery is the faithfulness

assumption---i.e. assuming that independencies found in the data are due to

separations in the true causal graph. This assumption can, however, be violated

in many ways, including xor connections, deterministic functions or cancelling

paths. In this work, we propose a weaker assumption that we call 2-adjacency

faithfulness. In contrast to adjacency faithfulness, which assumes that there

is no conditional independence between each pair of variables that are

connected in the causal graph, we only require no conditional independence

between a node and a subset of its Markov blanket that can contain up to two

nodes. Equivalently, we adapt orientation faithfulness to this setting. We

further propose a sound orientation rule for causal discovery that applies

under weaker assumptions. As a proof of concept, we derive a modified Grow and

Shrink algorithm that recovers the Markov blanket of a target node and prove

its correctness under strictly weaker assumptions than the standard

faithfulness assumption.

assumption---i.e. assuming that independencies found in the data are due to

separations in the true causal graph. This assumption can, however, be violated

in many ways, including xor connections, deterministic functions or cancelling

paths. In this work, we propose a weaker assumption that we call 2-adjacency

faithfulness. In contrast to adjacency faithfulness, which assumes that there

is no conditional independence between each pair of variables that are

connected in the causal graph, we only require no conditional independence

between a node and a subset of its Markov blanket that can contain up to two

nodes. Equivalently, we adapt orientation faithfulness to this setting. We

further propose a sound orientation rule for causal discovery that applies

under weaker assumptions. As a proof of concept, we derive a modified Grow and

Shrink algorithm that recovers the Markov blanket of a target node and prove

its correctness under strictly weaker assumptions than the standard

faithfulness assumption.