# Causal Discovery in Mixtures of Populations

arXiv: https://arxiv.org/abs/2311.07454 · HTML: https://mlsanity.com/paper/2311.07454/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 54 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Beyond the Low-Degree Algorithm: Mixtures of Subcubes and Their Applications](https://mlsanity.com/paper/1803.06521/) (2018)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Source Identification for Mixtures of Product Distributions](https://mlsanity.com/paper/2012.14540/) (2020)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [An Algorithm for Finding Minimum d-Separating Sets in Belief Networks](https://mlsanity.com/paper/1302.3549/) (2013)
- [Fast algorithm for overcomplete order-3 tensor decomposition](https://mlsanity.com/paper/2202.06442/) (2022)
- [Identification of Mixtures of Discrete Product Distributions in Near-Optimal Sample and Time Complexity](https://mlsanity.com/paper/2309.13993/) (2023)
- [Restricted Hidden Cardinality Constraints in Causal Models](https://mlsanity.com/paper/2109.05656/) (2021)

## Built on by (most cited first, 4 of 4)

- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Learning Discrete Latent Variable Structures with Tensor Rank Conditions](https://mlsanity.com/paper/2406.07020/) (2024)
- [Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence](https://mlsanity.com/paper/2604.07191/) (2026)
- [The Spectral Structure of Latent Treatment Effects](https://mlsanity.com/paper/2607.10926/) (2026)

## Abstract (arXiv)

Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.