# Linear causal disentanglement via higher-order cumulants

arXiv: https://arxiv.org/abs/2407.04605 · HTML: https://mlsanity.com/paper/2407.04605/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 72 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 27 of 27)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Identifiable Deep Generative Models via Sparse Decoding](https://mlsanity.com/paper/2110.10804/) (2021)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies](https://mlsanity.com/paper/2401.04890/) (2024)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Subspace power method for symmetric tensor decomposition](https://mlsanity.com/paper/1912.04007/) (2019)
- [A Commentary on the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/2007.14184/) (2020)
- [Anchored Discrete Factor Analysis](https://mlsanity.com/paper/1511.03299/) (2015)
- [Propensity Score Alignment of Unpaired Multimodal Data](https://mlsanity.com/paper/2404.01595/) (2024)
- [Invariance & Causal Representation Learning: Prospects and Limitations](https://mlsanity.com/paper/2312.03580/) (2023)
- [Towards Identifiable Latent Additive Noise Models](https://mlsanity.com/paper/2403.15711/) (2024)

## Built on by (most cited first, 1 of 1)

- [Causal Representation Meets Stochastic Modeling under Generic Geometry](https://mlsanity.com/paper/2602.05033/) (2026)

## Abstract (arXiv)

Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both independent component analysis and linear structural equation models. We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts, each given by an intervention on a latent variable. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions, generalizing previous work to allow more latent than observed variables. We give a constructive proof that computes parameters via a coupled tensor decomposition. For soft interventions, we find the equivalence class of latent graphs and parameters that are consistent with observed data, via the study of a system of polynomial equations. Our results hold assuming the existence of non-zero higher-order cumulants, which implies non-Gaussianity of variables.