## Abstract

One common task in many data sciences applications is to answer questions about the effect of new interventions, like: 'what would happen to Y if we make X equal to x while observing covariates Z = z?'. Formally, this is known as conditional effect identification, where the goal is to determine whether a post-interventional distribution is computable from the combination of an observational distribution and assumptions about the underlying domain represented by a causal diagram. A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available. In this paper, we assume as the input of the task a less informative structure known as a partial ancestral graph (PAG), which represents a Markov equivalence class of causal diagrams, learnable from observational data. We make the following contributions under this relaxed setting. First, we introduce a new causal calculus, which subsumes the current state-of-the-art, PAG-calculus. Second, we develop an algorithm for conditional effect identification given a PAG and prove it to be both sound and complete. In words, failure of the algorithm to identify a certain effect implies that this effect is not identifiable by any method. Third, we prove the proposed calculus to be complete for the same task.

Original language | English |
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Title of host publication | Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022 |

Editors | S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh |

Publisher | Neural Information Processing Systems Foundation |

Number of pages | 10 |

ISBN (Electronic) | 9781713871088 |

Publication status | Published - 2022 |

Event | 36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans Convention Center, New Orleans, United States Duration: 28 Nov 2022 → 9 Dec 2022 https://neurips.cc/Conferences/2022 https://openreview.net/group?id=NeurIPS.cc/2022/Conference https://proceedings.neurips.cc/paper_files/paper/2022 |

### Publication series

Name | Advances in Neural Information Processing Systems |
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Volume | 35 |

ISSN (Print) | 1049-5258 |

### Conference

Conference | 36th Conference on Neural Information Processing Systems, NeurIPS 2022 |
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Country/Territory | United States |

City | New Orleans |

Period | 28/11/22 → 9/12/22 |

Internet address |

## Scopus Subject Areas

- Computer Networks and Communications
- Information Systems
- Signal Processing