Generic Identifiability of Linear Structural Equation Models by Ancestor Decomposition

Abstract

Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modelling multivariate joint distributions. The 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 building upon the half-trek criterion. Underlying our new algorithm is the idea that ancestral subsets of vertices in the graph can be used to extend the applicability of a decomposition technique.

Identifiability of directed Gaussian graphical models with one latent source

“…While Theorems 6.1 and 6.2 may be useful in some contexts, models in which latent variables are parents to only some of the observables deserve a more in-depth treatment in future work. In particular, it would be natural to seek ways to combine the results of Stanghellini and Wermuth (2005) and the present paper with the work of Foygel et al (2012) and Drton and Weihs (2015).…”

Identifying dynamical time series model parameters from equilibrium samples, with application to gene regulatory networks

“…Seeking identifiability conditions has been the subject of a number of papers (Brito and Pearl, 2012;Drton and Weihs, 2016;Drton et al, 2011), and general conditions for this class of models are not known.…”

“…SEM, however, relates the variables without considering the time element. If boldX is the collection of random variables observed, then a linear structural equation model with Gaussian noise can be written as Seeking identifiability conditions has been the subject of a number of papers (Brito and Pearl, 2012; Drton andWeihs, 2016; Drton et al, 2011), and general conditions for this class of models are not known.…”

Experimental Design Issues in Big Data: The Question of Bias

“…We can also passively observe X 1 , X 2 , X 3 , X 4 . Note that the model is nonlinear in the parameters as 4 and also that X 4 is Gaussian if the {ε i } are Gaussian. One may not have to choose between a controlled experiment and passive observation.…”