Multi-task Learning of Order-Consistent Causal Graphs
This addresses the challenge of learning causal structures from related datasets, which is incremental but important for fields like bioinformatics or social sciences where multiple similar causal models exist.
The paper tackles the problem of discovering multiple related Gaussian directed acyclic graphs (DAGs) with consistent causal orders and sparse unions of supports, proposing a multi-task learning estimator that achieves better sample complexity for recovering causal orders and can recover non-identifiable DAGs, as validated in experiments.
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 $l_1/l_2$-regularized 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.