Contextual Directed Acyclic Graphs
This addresses the challenge of estimating DAG structures in machine learning for populations with heterogeneous data, representing an incremental advance by extending single-graph methods to context-dependent settings.
The paper tackles the problem of learning directed acyclic graphs (DAGs) that vary across individuals based on contextual features, proposing a neural network with a novel projection layer to ensure sparsity and acyclicity, and shows it can recover true context-specific graphs where existing methods fail.
Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adjacency matrix. The neural network is equipped with a novel projection layer that ensures the output matrices are sparse and satisfy a recently developed characterization of acyclicity. We devise a scalable computational framework for learning contextual DAGs and provide a convergence guarantee and an analytical gradient for backpropagating through the projection layer. Our experiments suggest that the new approach can recover the true context-specific graph where existing approaches fail.