# Algebraic Equivalence of Linear Structural Equation Models

arXiv: https://arxiv.org/abs/1807.03527 · HTML: https://mlsanity.com/paper/1807.03527/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2018.

## Built on by (most cited first, 1 of 1)

- [Graphical Representations for Algebraic Constraints of Linear Structural Equations Models](https://mlsanity.com/paper/2208.00926/) (2022)

## Abstract (arXiv)

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.