# Partially Observed Structural Causal Models

arXiv: https://arxiv.org/abs/2605.03268 · HTML: https://mlsanity.com/paper/2605.03268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 12 of 12)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders](https://mlsanity.com/paper/1807.03024/) (2018)
- [Identifying Causal Effects via Context-specific Independence Relations](https://mlsanity.com/paper/2009.09768/) (2020)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Causal Inference with a Graphical Hierarchy of Interventions](https://mlsanity.com/paper/1411.2127/) (2014)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)
- [A General Identification Algorithm For Data Fusion Problems Under Systematic Selection](https://mlsanity.com/paper/2404.06602/) (2024)

## Abstract (arXiv)

Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive Markov kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.