# Multi-Level Cause-Effect Systems

arXiv: https://arxiv.org/abs/1512.07942 · HTML: https://mlsanity.com/paper/1512.07942/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2015.

## Built on by (most cited first, 30 of 30)

- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Image-based Treatment Effect Heterogeneity](https://mlsanity.com/paper/2206.06417/) (2022)
- [Causal models in string diagrams](https://mlsanity.com/paper/2304.07638/) (2023)
- [On the Equivalence of Causal Models: A Category-Theoretic Approach](https://mlsanity.com/paper/2201.06981/) (2022)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Towards a Grounded Theory of Causation for Embodied AI](https://mlsanity.com/paper/2206.13973/) (2022)
- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [Integrating Earth Observation Data into Causal Inference: Challenges and Opportunities](https://mlsanity.com/paper/2301.12985/) (2023)
- [Meaningful Causal Aggregation and Paradoxical Confounding](https://mlsanity.com/paper/2304.11625/) (2023)
- [Nonlinear Causal Discovery for Grouped Data](https://mlsanity.com/paper/2506.05120/) (2025)
- [Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering](https://mlsanity.com/paper/2511.01396/) (2025)
- [Encoding Causal Macrovariables](https://mlsanity.com/paper/2111.14724/) (2021)
- [Estimating Causal Effects Under Image Confounding Bias with an Application to Poverty in Africa](https://mlsanity.com/paper/2206.06410/) (2022)
- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [Causal reasoning in difference graphs](https://mlsanity.com/paper/2411.01292/) (2024)
- [Causal DAG Summarization (Full Version)](https://mlsanity.com/paper/2504.14937/) (2025)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Joint Causal Structure and Cluster Discovery Using Variational Inference](https://mlsanity.com/paper/2608.22212/) (2026)
- [Causal Feature Learning in the Social Sciences](https://mlsanity.com/paper/2503.12784/) (2025)
- [Validating Causal Abstraction Metrics on Simulated Complex Systems](https://mlsanity.com/paper/2607.00267/) (2026)

## Abstract (arXiv)

We present a domain-general account of causation that applies to settings in which macro-level causal relations between two systems are of interest, but the relevant causal features are poorly understood and have to be aggregated from vast arrays of micro-measurements. Our approach generalizes that of Chalupka et al. (2015) to the setting in which the macro-level effect is not specified. We formalize the connection between micro- and macro-variables in such situations and provide a coherent framework describing causal relations at multiple levels of analysis. We present an algorithm that discovers macro-variable causes and effects from micro-level measurements obtained from an experiment. We further show how to design experiments to discover macro-variables from observational micro-variable data. Finally, we show that under specific conditions, one can identify multiple levels of causal structure. Throughout the article, we use a simulated neuroscience multi-unit recording experiment to illustrate the ideas and the algorithms.