Learning Optimal Causal Graphs with Exact Search

Discovering graphical models over very general model spaces with high accuracy requires optimally combining conflicting (in)dependence constraints in sample data, and thus results in a computationally hard combinatorial optimization problem. Recent advances in exact algorithmic approaches in this constraint-based setting build upon off-the-shelf declarative optimization solvers. In this paper, we propose the first truly specialized exact search algorithm for optimal causal graphs in a general model space, allowing both cycles and latent confounding variables. Our problem-oriented approach enables directly incorporating domain knowledge for developing a wider range of specialized search techniques for the problem, including problem-specific propagators, branching heuristics, and bounding techniques, as well as directly incorporating different constraints on the model space, such as sparsity and acyclicity constraints. We empirically evaluate a first implementation of the approach, showing that it clearly outperforms current state of art in exact constraint-based causal discovery on real-world instances.