Algebraic Equivalence of Linear Structural Equation Models
This work addresses foundational issues in causal discovery for researchers, offering incremental advances in handling algebraic constraints.
The paper tackles the open problems of enumerating algebraic constraints in linear structural equation models and deciding equivalence between graphs, showing that the half-trek criterion can address both. It applies this to model selection, finding significant accuracy improvements when incorporating algebraic constraints.
Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statistical model. We show how the half-trek criterion can be used to make progress in both of these problems. We apply our theoretical results to a small-scale model selection problem, and find that taking the additional algebraic constraints into account may lead to significant improvements in model selection accuracy.