Identifying Direct Causal Effects in Latent Factor Models by Accounting for Unidentified Parents

2026-05-27

AI Summary

This study addresses the challenge of identifying direct causal effects among observed variables in densely confounded linear structural equation models with latent variables, where conventional methods often fail. The authors propose a novel identification criterion that explicitly models latent variables, employs a recursive identification strategy, and systematically handles unidentified causal parents. By transforming the combinatorial search problem into an efficient network flow computation, the method substantially enhances the identifiability of direct causal effects in dense confounding settings. Accompanied by an open-source algorithmic implementation, this approach combines theoretical rigor with practical utility for causal inference in complex observational data.

Abstract

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct causal effects between the observed variables of interest by providing (rational) formulas in the observed covariances. Most prior identification approaches operate in the latent projection framework, where latent variables are projected away into dependent error terms. However, when the observed variables are densely confounded, even if only by a few latent variables, the projection-based approaches are unable to certify identifiability of most effects. For such problems, approaches that explicitly use the latent variables are more effective, but algorithms that were recently proposed for this purpose often remain inconclusive for denser causal graphs. We develop a new identification criterion that is able to better handle dense graphs by leveraging the key insight that recursive identification schemes can be generalized by explicitly accounting for causal parents with (yet) unidentified direct effects. Combinatorial search problems in our new criterion can be tackled with the help of network-flow computations, leading to a practical useful algorithmic tool that we also make available in software.

Problem

• causal identification
• latent variables
• structural equation models
• direct causal effects
• confounding

Innovation

• causal identification
• latent factor models
• network flow
• structural equation models
• direct causal effects