Robust estimation of Gaussian linear structural equation models with equal error variances

This study develops a new approach to learning Gaussian linear structural equation models (SEMs) with equal error variances from possibly corrupted observations by outliers. More precisely, we consider the two types of corrupted Gaussian linear SEMs depending on the outlier type and develop a structure learning algorithm for the models. The proposed algorithm consists of two steps in which the effect of outliers is eliminated: Step (1) infers the ordering using conditional variances, and Step (2) estimates the presence of edges using conditional independence relationships. Various numerical experiments verify that the proposed algorithm is empirically consistent even when corrupted samples exist. It is further confirmed that the proposed algorithm performs better than the state-of-the-art US, GDS, PC, and GES algorithms in noisy data settings. Through the corrupted real examination marks data, we also demonstrate that the proposed algorithm is well-suited to capturing the interpretable relationships between subjects.