Partially Observed Structural Causal Models

2026-05-04

AI Summary

This work addresses the limitations of traditional structural causal models in settings where latent variables jointly influence both causal structure and mechanisms, rendering endogenous graphs and fine-grained interventions intractable. The authors propose Partially Observable Structural Causal Models (POSCMs), which introduce a latent context that jointly determines the interaction structure and generative mechanisms among observed variables. They formulate a multi-level intervention framework encompassing nodes, edges, and context, thereby extending structural causal models to endogenous graph settings for the first time and enabling surgical edge interventions. A theoretical foundation for identifiability of both structure and mechanisms is established. Leveraging Kolmogorov–Arnold–Sprecher decomposition for explicit parametrization of node mechanisms, experiments on a simulated human retinal circuit demonstrate that node-only interventions fail to disentangle structure–mechanism confounding induced by latent edges, whereas targeted edge interventions accurately recover synaptic input–output relationships.

Abstract

Here we introduce Partially Observed Structural Causal Models (POSCMs) that formalize causal systems where latent contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs provide an extension of structural causal models (SCMs), as a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level context and endogenous variable interventions. To enable surgical edge interventions, we adopt a Kolmogorov-Arnold-Sprecher edge-functional decomposition, an existence theorem for representing each node mechanism as a sum of univariate functions of its parents, yielding an explicit parametrization of dyadic functional contributions. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We empirically validate these predictions in a biophysically detailed virtual human retina simulator, constructing intervention protocols that (i) reproduce the non-identifiability predicted when context is latent and no context-level interventions are available, (ii) exhibit structure-mechanism confounding under latent edges when only node interventions are observed, and (iii) recover synaptic input-output relationships via targeted node interventions, consistent with our positive kernel identifiability result. Our work generalizes SCMs in a way that allows it to work in a world closer to the one we live in.

Problem

• Partially Observed Structural Causal Models
• latent contexts
• causal identifiability
• endogenous graphs
• structural causal models

Innovation

• Partially Observed Structural Causal Models
• endogenous graphs
• surgical edge interventions
• Kolmogorov-Arnold-Sprecher decomposition
• identifiability theory