Discovering causal graphs with cycles and latent confounders: An exact branch-and-bound approach

Understanding causal relationships is a central challenge in many research endeavours. Recent research has shown the importance of accounting for feedback (cycles) and latent confounding variables, as they are prominently present in many data analysis settings. However, allowing for cycles and latent confounders makes the structure learning task especially challenging. The constraint-based approach is able to learn causal graphs even over such general search spaces, but to obtain high accuracy, the conflicting (in)dependence information in sample data need to be resolved optimally. In this work, we develop a new practical algorithmic approach to solve this computationally challenging combinatorial optimization problem. While recent advances in exact algorithmic approaches for constraint-based causal discovery build upon off-the-shelf declarative optimization solvers, we propose a first specialized branch-and-bound style exact search algorithm. 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 and reasoning rules, and branching heuristics together with linear programming based bounding techniques, as well as directly incorporating different constraints on the search space, such as sparsity and acyclicity constraints. We empirically evaluate our implementation of the approach, showing that it outperforms current state of art in exact constraint-based causal discovery on real-world instances.