## Abstract

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.

Original language | English |
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Pages (from-to) | 1022-1030 |

Number of pages | 9 |

Journal | Proceedings of Machine Learning Research |

Volume | 180 |

State | Published - 2022 |

Externally published | Yes |

Event | 38th Conference on Uncertainty in Artificial Intelligence, UAI 2022 - Eindhoven, Netherlands Duration: 1 Aug 2022 → 5 Aug 2022 |