# Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding

arXiv: https://arxiv.org/abs/2407.07934 · HTML: https://mlsanity.com/paper/2407.07934/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 10 Jul 2024.

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

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders](https://mlsanity.com/paper/1807.03024/) (2018)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias](https://mlsanity.com/paper/1901.00433/) (2019)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [Identifiability of Direct Effects from Summary Causal Graphs](https://mlsanity.com/paper/2306.16958/) (2023)
- [When does the ID algorithm fail?](https://mlsanity.com/paper/2307.03750/) (2023)
- [Causal Inference on Process Graphs, Part II: Causal Structure and Effect Identification](https://mlsanity.com/paper/2406.17422/) (2024)

## Built on by (most cited first, 9 of 9)

- [Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering](https://mlsanity.com/paper/2511.01396/) (2025)
- [Identifying Macro Causal Effects in a C-DMG over ADMGs](https://mlsanity.com/paper/2504.01551/) (2025)
- [Identifying Macro Causal Effects in C-DMGs over DMGs](https://mlsanity.com/paper/2506.19650/) (2025)
- [Note on the identification of total effect in Cluster-DAGs with cycles](https://mlsanity.com/paper/2504.07921/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Average Controlled and Average Natural Micro Direct Effects in Summary Causal Graphs](https://mlsanity.com/paper/2410.23975/) (2024)
- [Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions](https://mlsanity.com/paper/2508.21742/) (2025)
- [On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphs](https://mlsanity.com/paper/2512.18315/) (2025)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Understanding causal relations in dynamic systems is essential in epidemiology. While causal inference methods have been extensively studied, they often rely on fully specified causal graphs, which may not always be available in complex dynamic systems. Partially specified causal graphs, and in particular summary causal graphs (SCGs), provide a simplified representation of causal relations between time series when working spacio-temporal data, omitting temporal information and focusing on causal structures between clusters of of temporal variables. Unlike fully specified causal graphs, SCGs can contain cycles, which complicate their analysis and interpretation. In addition, their cluster-based nature introduces new challenges concerning the types of queries of interest: macro queries, which involve relationships between clusters represented as vertices in the graph, and micro queries, which pertain to relationships between variables that are not directly visible through the vertices of the graph. In this paper, we first clearly distinguish between macro conditional independencies and micro conditional independencies and between macro total effects and micro total effects. Then, we demonstrate the soundness and completeness of the d-separation to identify macro conditional independencies in SCGs. Furthermore, we establish that the do-calculus is sound and complete for identifying macro total effects in SCGs. Finally, we give a graphical characterization for the non-identifiability of macro total effects in SCGs.