Partially Observed Structural Causal Models

TL;DR

This paper introduces Partially Observed Structural Causal Models (POSCMs), extending SCMs to handle latent contexts affecting structure and mechanisms, with theoretical and empirical validation in a virtual retina simulator.

Contribution

It formalizes POSCMs for causal systems with latent contexts, providing an intervention hierarchy, an edge-functional decomposition, and an identifiability theory, validated through biophysical simulations.

Findings

Reproduces non-identifiability with latent context and no context interventions.

Shows structure-mechanism confounding under latent edges with only node interventions.

Recovers synaptic input-output relationships with targeted node interventions.

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.