Robust Identifiability in Linear Structural Equation Models of Causal Inference

TL;DR

This paper investigates the conditions under which parameters in linear structural equation models can be robustly identified from observational data, extending prior work to broader classes of models and validating findings empirically.

Contribution

It provides new sufficient conditions for robust identifiability in bow-free linear SEMs, removing previous restrictions and demonstrating high-probability applicability.

Findings

Robust identifiability conditions hold for a large class of bow-free models.

Existing algorithms achieve robust identifiability under these conditions.

Empirical validation on simulated and real datasets supports theoretical results.

Abstract

In this work, we consider the problem of robust parameter estimation from observational data in the context of linear structural equation models (LSEMs). LSEMs are a popular and well-studied class of models for inferring causality in the natural and social sciences. One of the main problems related to LSEMs is to recover the model parameters from the observational data. Under various conditions on LSEMs and the model parameters the prior work provides efficient algorithms to recover the parameters. However, these results are often about generic identifiability. In practice, generic identifiability is not sufficient and we need robust identifiability: small changes in the observational data should not affect the parameters by a huge amount. Robust identifiability has received far less attention and remains poorly understood. Sankararaman et al. (2019) recently provided a set of sufficient conditions on parameters under which robust identifiability is feasible. However, a limitation of their work is that their results only apply to a small sub-class of LSEMs, called ``bow-free paths.'' In this work, we significantly extend their work along multiple dimensions. First, for a large and well-studied class of LSEMs, namely ``bow free'' models, we provide a sufficient condition on model parameters under which robust identifiability holds, thereby removing the restriction of paths required by prior work. We then show that this sufficient condition holds with high probability which implies that for a large set of parameters robust identifiability holds and that for such parameters, existing algorithms already achieve robust identifiability. Finally, we validate our results on both simulated and real-world datasets.