# Causal Representation Learning Made Identifiable by Grouping of Observational Variables

arXiv: https://arxiv.org/abs/2310.15709 · HTML: https://mlsanity.com/paper/2310.15709/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 111 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)

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

- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Everything, Everywhere, All at Once: Is Mechanistic Interpretability Identifiable?](https://mlsanity.com/paper/2502.20914/) (2025)
- [On the Identification of Temporally Causal Representation with Instantaneous Dependence](https://mlsanity.com/paper/2405.15325/) (2024)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [SmartCLIP: Modular Vision-language Alignment with Identification Guarantees](https://mlsanity.com/paper/2507.22264/) (2025)
- [Causal Representation Learning from Multimodal Biomedical Observations](https://mlsanity.com/paper/2411.06518/) (2024)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [Towards Identifiability of Hierarchical Temporal Causal Representation Learning](https://mlsanity.com/paper/2510.18310/) (2025)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Mechanistic Interpretability Needs Philosophy](https://mlsanity.com/paper/2506.18852/) (2025)
- [LLM Interpretability with Identifiable Temporal-Instantaneous Representation](https://mlsanity.com/paper/2509.23323/) (2025)
- [Causal Representation Learning from General Environments under Nonparametric Mixing](https://mlsanity.com/paper/2604.23800/) (2026)
- [Synergy Between Sufficient Changes and Sparse Mixing Procedure for Disentangled Representation Learning](https://mlsanity.com/paper/2503.00639/) (2025)
- [Modeling Unseen Environments with Language-guided Composable Causal Components in Reinforcement Learning](https://mlsanity.com/paper/2505.08361/) (2025)
- [Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability](https://mlsanity.com/paper/2510.17040/) (2025)
- [Distribution Shift Is Key to Learning Invariant Prediction](https://mlsanity.com/paper/2601.12296/) (2026)
- [Discovering Latent Causal Graphs from Spatiotemporal Data](https://mlsanity.com/paper/2411.05331/) (2024)
- [Causal Representation Learning with Observational Grouping for CXR Classification](https://mlsanity.com/paper/2506.20582/) (2025)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Understanding Catastrophic Interference: On the Identifibility of Latent Representations](https://mlsanity.com/paper/2509.23027/) (2025)
- [Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing](https://mlsanity.com/paper/2604.13218/) (2026)
- [Operationalizing Quantized Disentanglement](https://mlsanity.com/paper/2511.20927/) (2025)
- [CURVE: Learning Causality-Inspired Invariant Representations for Robust Scene Understanding via Uncertainty-Guided Regularization](https://mlsanity.com/paper/2601.20355/) (2026)
- [Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations](https://mlsanity.com/paper/2602.24278/) (2026)
- [Diverse Dictionary Learning](https://mlsanity.com/paper/2604.17568/) (2026)
- [Identifiable Multimodal Causal Representation Learning under Partial Latent Sharing](https://mlsanity.com/paper/2605.19135/) (2026)
- [Position: Prioritize Identifying Structure, Not Complex Models, for Scientific Discovery](https://mlsanity.com/paper/2606.02632/) (2026)
- [Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts](https://mlsanity.com/paper/2606.28228/) (2026)
- [MoVA: Learning Asymmetric Dual Projections for Modular Long Video-Text Alignment](https://mlsanity.com/paper/2607.00858/) (2026)
- [Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States](https://mlsanity.com/paper/2607.19531/) (2026)

## Abstract (arXiv)

A topic of great current interest is Causal Representation Learning (CRL), whose goal is to learn a causal model for hidden features in a data-driven manner. Unfortunately, CRL is severely ill-posed since it is a combination of the two notoriously ill-posed problems of representation learning and causal discovery. Yet, finding practical identifiability conditions that guarantee a unique solution is crucial for its practical applicability. Most approaches so far have been based on assumptions on the latent causal mechanisms, such as temporal causality, or existence of supervision or interventions; these can be too restrictive in actual applications. Here, we show identifiability based on novel, weak constraints, which requires no temporal structure, intervention, nor weak supervision. The approach is based on assuming the observational mixing exhibits a suitable grouping of the observational variables. We also propose a novel self-supervised estimation framework consistent with the model, prove its statistical consistency, and experimentally show its superior CRL performances compared to the state-of-the-art baselines. We further demonstrate its robustness against latent confounders and causal cycles.