Reproduce “Causal Discovery in Linear Latent Variable Models Subject to Measurement Error” on OpenResearch

About this paper

Yuqin Yang, AmirEmad Ghassami, Mohamed Nafea, Negar Kiyavash, Kun Zhang, Ilya Shpitser

This research establishes a formal connection and identifiability mapping between linear structural equation models subject to measurement error (SEM-ME) and those with unobserved root causes (SEM-UR). It characterizes identifiability through Ancestral Ordered Grouping (AOG) and Direct Ordered Grouping (DOG) equivalence classes, showing that the true causal structure within the DOG class is the sparsest among observationally equivalent models and demonstrating superior empirical performance over baseline methods.

Key insights

• A fundamental connection exists between Linear Structural Equation Models with Measurement Error (SEM-ME) and those with Unobserved Roots (SEM-UR), allowing identifiability results to be translated between these two model types.
• Under specific faithfulness and separability assumptions, the structural graph of a SEM-UR model can be uniquely identified, significantly relaxing previous graphical conditions for latent variable models.
• The true causal structure (within its Direct Ordered Grouping equivalence class) is provably the sparsest among observationally equivalent models, providing a principled basis for using sparsity in causal discovery.

Summary by alphaXiv.