Learning Directed Acyclic Graphs from Partial Orderings
This work addresses a key bottleneck in causal inference for researchers and practitioners by enabling more efficient DAG learning with partial prior knowledge, though it is incremental as it builds on existing methods for complete orderings.
The paper tackles the problem of learning directed acyclic graphs (DAGs) from observational data when only a partial causal ordering of variables is available, proposing a general estimation framework with efficient algorithms for low- and high-dimensional settings, and demonstrates advantages through numerical studies.
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information, the direction of edges may not be estimable from observational data. In contrast, given a complete causal ordering of the variables, the problem can be solved efficiently, even in high dimensions. In this paper, we consider the intermediate problem of learning DAGs when a partial causal ordering of variables is available. We propose a general estimation framework for leveraging the partial ordering and present efficient estimation algorithms for low- and high-dimensional problems. The advantages of the proposed framework are illustrated via numerical studies.