Graphical Representations for Algebraic Constraints of Linear Structural Equations Models

Abstract

The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical for many purposes. In this paper, we present a graphical notation for many of these polynomial constraints. The expressive power of this notation is investigated both theoretically and empirically.

To appear in the proceedings of the 11th International Conference on Probabilistic Graphical Models (PGM 2022)