# From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables

arXiv: https://arxiv.org/abs/2604.22416 · HTML: https://mlsanity.com/paper/2604.22416/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Foundations of Causal Discovery on Groups of Variables](https://mlsanity.com/paper/2306.07047/) (2023)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Vector causal inference between two groups of variables](https://mlsanity.com/paper/2209.14283/) (2022)
- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)
- [Local search for efficient causal effect estimation](https://mlsanity.com/paper/2007.10014/) (2020)
- [Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairs](https://mlsanity.com/paper/2310.17816/) (2023)
- [Discovery and inference of a causal network with hidden confounding](https://mlsanity.com/paper/2309.09420/) (2023)
- [Towards Efficient Local Causal Structure Learning](https://mlsanity.com/paper/2103.00378/) (2021)
- [Local Causal Discovery for Structural Evidence of Direct Discrimination](https://mlsanity.com/paper/2405.14848/) (2024)
- [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)
- [Identifying Macro Causal Effects in a C-DMG over ADMGs](https://mlsanity.com/paper/2504.01551/) (2025)
- [Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables](https://mlsanity.com/paper/2411.16315/) (2024)
- [Identifying Macro Causal Effects in C-DMGs over DMGs](https://mlsanity.com/paper/2506.19650/) (2025)

## Abstract (arXiv)

Latent variables pose a fundamental obstacle to both causal discovery and inference. Local approaches exploiting direct neighborhood relations provide little beyond immediate dependencies. Cluster-level methods, though capable of broader reasoning, generally require cluster assignments or causal sufficiency in advance, conditions that are rarely satisfied in practice. Applying single-variable discovery at cluster resolution violates these conditions and thereby produces systematic bias. L2C (Local to Cluster Causal Abstraction) learns cluster structure from local causal patterns without manual variable-to-cluster mapping. The framework rests on a cluster reduction theorem: each cluster can be represented by at most three micro-variables, with no loss of macro-level identifiability. In the presence of latent variables, local discovery on maximal ancestral graphs recovers direct causes, effects, and V-structures, followed by cluster-level inference through a corresponding calculus on the resulting graph. Macro causal effects are formulated as joint interventions on the micro-variables within each target cluster. The framework is sound, atomically complete, and polynomially bounded. L2C establishes a direct connection from local micro-level information to macro causal reasoning in settings where clusters are unknown and latent variables are unavoidable.