Polynomial Constraints in Causal Bayesian Networks
This work addresses the problem of distinguishing and testing causal models for researchers in causal inference, though it appears incremental with complexity reductions and preliminary algebraic insights.
The authors tackled the problem of generating polynomial equality constraints for causal Bayesian networks with hidden variables using implicitization, showing how to reduce complexity to make the problem tractable in certain networks. They provided preliminary results on the algebraic structure of these constraints.
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce the complexity of the implicitization problem and make the problem tractable in certain causal Bayesian networks. We also show some preliminary results on the algebraic structure of polynomial constraints. The results have applications in distinguishing between causal models and in testing causal models with combined observational and experimental data.