# Identifiability Guarantees for Causal Disentanglement from Soft Interventions

arXiv: https://arxiv.org/abs/2307.06250 · HTML: https://mlsanity.com/paper/2307.06250/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 73 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 30 of 38)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (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)
- [Causal Machine Learning: A Survey and Open Problems](https://mlsanity.com/paper/2206.15475/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [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)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Sliced Wasserstein Generative Models](https://mlsanity.com/paper/1904.05408/) (2019)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)

## Built on by (most cited first, 30 of 84)

- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models](https://mlsanity.com/paper/2402.09236/) (2024)
- [Multi-Domain Causal Representation Learning via Weak Distributional Invariances](https://mlsanity.com/paper/2310.02854/) (2023)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Identifying Representations for Intervention Extrapolation](https://mlsanity.com/paper/2310.04295/) (2023)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)
- [Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions](https://mlsanity.com/paper/2311.02695/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity](https://mlsanity.com/paper/2311.12267/) (2023)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [All or None: Identifiable Linear Properties of Next-token Predictors in Language Modeling](https://mlsanity.com/paper/2410.23501/) (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)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Smoke and Mirrors in Causal Downstream Tasks](https://mlsanity.com/paper/2405.17151/) (2024)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Season combinatorial intervention predictions with Salt & Peper](https://mlsanity.com/paper/2404.16907/) (2024)
- [An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis](https://mlsanity.com/paper/2311.18048/) (2023)
- [Language Agents Meet Causality -- Bridging LLMs and Causal World Models](https://mlsanity.com/paper/2410.19923/) (2024)
- [Automated Discovery of Pairwise Interactions from Unstructured Data](https://mlsanity.com/paper/2409.07594/) (2024)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (2024)
- [CausalVLBench: Benchmarking Visual Causal Reasoning in Large Vision-Language Models](https://mlsanity.com/paper/2506.11034/) (2025)
- [From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?](https://mlsanity.com/paper/2512.15134/) (2025)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Debiasing Reward Models by Representation Learning with Guarantees](https://mlsanity.com/paper/2510.23751/) (2025)
- [Invariance & Causal Representation Learning: Prospects and Limitations](https://mlsanity.com/paper/2312.03580/) (2023)

## Abstract (arXiv)

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.