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Multi-Task Learning of Order-Consistent Causal Graphs
  • Xinshi Chen, Georgia Institute of Technology
  • Haoran Sun, Georgia Institute of Technology
  • Caleb Ellington, Carnegie Mellon University
  • Eric Xing, Carnegie Mellon University & Mohamed bin Zayed University of Artificial University
  • Le Song, BioMap & Mohamed bin Zayed University of Artificial Intelligence
Document Type

We consider the problem of discovering K related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a l1/l2regularized maximum likelihood estimator (MLE) for learning K linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments. © 2021, CC BY-NC-SA.

Publication Date

Preprint: arXiv

  • Archived with thanks to arXiv
  • Preprint license: CC by NC-SA
  • Uploaded 24 March 2022
Citation Information
X. Chen, H. Sun, C. Ellington, E. Xing, and L. Song, "Multi-task learning of order-consistent causal graphs," 2021, arXiv:2111.02545