Generic Identifiability of Linear Structural Equation Models by Ancestor Decomposition

TL;DR

This paper introduces a new algorithm for determining the generic identifiability of parameters in linear structural equation models using ancestor decomposition, extending previous methods to improve analysis of mixed graph models.

Contribution

It presents an extended algorithm leveraging ancestral subsets for better identifiability analysis in linear SEMs, building on prior work by Foygel, Draisma, and Drton.

Findings

Algorithm successfully extends previous methods.

Improves identifiability analysis for mixed graph models.

Utilizes ancestral decomposition for enhanced accuracy.

Abstract

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both directed and bidirected edges representing the linear relationships and correlations between noise terms, respectively. A question of interest for these models is that of parameter identifiability, whether or not it is possible to recover edge coefficients from the joint covariance matrix of the random variables. For the problem of determining generic parameter identifiability, we present an algorithm that extends an algorithm from prior work by Foygel, Draisma, and Drton (2012). The main idea underlying our new algorithm is the use of ancestral subsets of vertices in the graph in application of a decomposition idea of Tian (2005).