Federated Causal Discovery with Additive Noise Models
Abstract: Causal discovery aims to learn a causal graph from observational data. To date, most causal discovery methods require data to be stored in a central server. However, data owners gradually refuse to share their personalized data to avoid privacy leakage, making this task more troublesome by cutting off the first step. A puzzle arises: how do we infer causal relations from decentralized data? In this paper, focusing on the additive noise models (ANMs) assumption of data, we take the first step in developing a gradient-based learning framework named DAG-Shared Federated Causal Discovery (DS-FCD), which can learn the causal graph without directly touching the local data and naturally handle the data heterogeneity caused by causal mechanism or noise shift. DS-FCD benefits from a two-level structure of each local model. The first level structure learns the causal graph and communicates with the server to get the model information from other clients during the learning procedure, while the second level structure approximates the causal mechanisms and personally updates from its own data to accommodate the data heterogeneity. Moreover, DS-FCD formulates the overall learning task as a continuous optimization problem by taking advantage of an equality acyclicity constraint, which can be solved by gradient descent methods. Extensive experiments on both synthetic and real-world datasets verify the efficacy of the proposed method.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We have addressed the comments by reviewers. Specifically:
1. Chang some statements for clarification and consistency.
2. Clarify our setup and algorithm procedures.
3. Move some contents from Appendix to the main text.
4. Add some discussions and visualizations in the Appendix.
5. Add the convergence analysis in the Appendix.
Assigned Action Editor: ~Novi_Quadrianto1
Submission Number: 163
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