Learning Optimal Causal Graphs with Exact Search
; Proceedings of the Ninth International Conference on Probabilistic Graphical Models, PMLR 72:344-355, 2018.
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.