# Unpaired Multi-Domain Causal Representation Learning

arXiv: https://arxiv.org/abs/2302.00993 · HTML: https://mlsanity.com/paper/2302.00993/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 76 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Self-Supervised Representation Learning: Introduction, Advances and Challenges](https://mlsanity.com/paper/2110.09327/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Function Classes for Identifiable Nonlinear Independent Component Analysis](https://mlsanity.com/paper/2208.06406/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modeling](https://mlsanity.com/paper/2211.03553/) (2022)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [Group Factor Analysis](https://mlsanity.com/paper/1411.5799/) (2014)
- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Causal Discovery with Multi-Domain LiNGAM for Latent Factors](https://mlsanity.com/paper/2009.09176/) (2020)
- [Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models](https://mlsanity.com/paper/2210.11021/) (2022)
- [Independent Vector Analysis: Identification Conditions and Performance Bounds](https://mlsanity.com/paper/1303.7474/) (2013)
- [Multi-View Independent Component Analysis with Shared and Individual Sources](https://mlsanity.com/paper/2210.02083/) (2022)
- [Shared Independent Component Analysis for Multi-Subject Neuroimaging](https://mlsanity.com/paper/2110.13502/) (2021)
- [Multi-Domain Translation by Learning Uncoupled Autoencoders](https://mlsanity.com/paper/1902.03515/) (2019)
- [Non-Independent Components Analysis](https://mlsanity.com/paper/2206.13668/) (2022)

## Built on by (most cited first, 30 of 32)

- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [Causal Representation Learning from Multimodal Biomedical Observations](https://mlsanity.com/paper/2411.06518/) (2024)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (2024)
- [Propensity Score Alignment of Unpaired Multimodal Data](https://mlsanity.com/paper/2404.01595/) (2024)
- [Toward the Identifiability of Comparative Deep Generative Models](https://mlsanity.com/paper/2401.15903/) (2024)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Conditionally Invariant Representation Learning for Disentangling Cellular Heterogeneity](https://mlsanity.com/paper/2307.00558/) (2023)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [Causal Structure and Representation Learning with Biomedical Applications](https://mlsanity.com/paper/2511.04790/) (2025)
- [Score-Based Causal Discovery of Latent Variable Causal Models](https://mlsanity.com/paper/2605.20396/) (2026)
- [Contrastive independent component analysis](https://mlsanity.com/paper/2407.02357/) (2024)
- [Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions](https://mlsanity.com/paper/2411.03755/) (2024)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Content-Style Identification via Differential Independence](https://mlsanity.com/paper/2605.17827/) (2026)
- [Unsupervised discovery of the shared and private geometry in multi-view data](https://mlsanity.com/paper/2408.12091/) (2024)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Nonlinear multi-study sparse factor analysis](https://mlsanity.com/paper/2601.18128/) (2026)
- [MultiLoReFT: Decoupling Shared and Modality-Specific Subspaces in Multimodal Learning via Low-Rank Representation Fine-Tuning](https://mlsanity.com/paper/2607.16789/) (2026)
- [Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms](https://mlsanity.com/paper/2502.20115/) (2025)
- [Trek-Based Parameter Identification for Linear Causal Models With Arbitrarily Structured Latent Variables](https://mlsanity.com/paper/2507.18170/) (2025)
- [PersonaX: Multimodal Datasets with LLM-Inferred Behavior Traits](https://mlsanity.com/paper/2509.11362/) (2025)
- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)
- [Identifiable Multimodal Causal Representation Learning under Partial Latent Sharing](https://mlsanity.com/paper/2605.19135/) (2026)
- [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026)

## Abstract (arXiv)

The goal of causal representation learning is to find a representation of data that consists of causally related latent variables. We consider a setup where one has access to data from multiple domains that potentially share a causal representation. Crucially, observations in different domains are assumed to be unpaired, that is, we only observe the marginal distribution in each domain but not their joint distribution. In this paper, we give sufficient conditions for identifiability of the joint distribution and the shared causal graph in a linear setup. Identifiability holds if we can uniquely recover the joint distribution and the shared causal representation from the marginal distributions in each domain. We transform our identifiability results into a practical method to recover the shared latent causal graph.