# Towards Identifiable Latent Additive Noise Models

arXiv: https://arxiv.org/abs/2403.15711 · HTML: https://mlsanity.com/paper/2403.15711/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 84 references that are in the map.
- First posted on arXiv 23 Mar 2024.

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

- [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)
- [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)
- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [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)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (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)
- [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)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning](https://mlsanity.com/paper/2107.00848/) (2021)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [CausalVAE: Structured Causal Disentanglement in Variational Autoencoder](https://mlsanity.com/paper/2004.08697/) (2020)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [Meta-Learning for Few-Shot Land Cover Classification](https://mlsanity.com/paper/2004.13390/) (2020)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [General Identifiability and Achievability for Causal Representation Learning](https://mlsanity.com/paper/2310.15450/) (2023)

## Built on by (most cited first, 5 of 5)

- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?](https://mlsanity.com/paper/2503.08980/) (2025)
- [On the Value of Cross-Modal Misalignment in Multimodal Representation Learning](https://mlsanity.com/paper/2504.10143/) (2025)
- [What Makes a Representation Good for Single-Cell Perturbation Prediction?](https://mlsanity.com/paper/2605.19343/) (2026)
- [Linear causal disentanglement via higher-order cumulants](https://mlsanity.com/paper/2407.04605/) (2024)

## Abstract (arXiv)

Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required for identifiability and by challenges in applying them to real-world settings. Most current approaches are applicable only to relatively restrictive model classes, such as linear or polynomial models, which limits their flexibility and robustness in practice. One promising approach to this problem seeks to address these issues by leveraging changes in causal influences among latent variables. In this vein we propose a more general and relaxed framework than typically applied, formulated by imposing constraints on the function classes applied. Within this framework, we establish partial identifiability results under weaker conditions, including scenarios where only a subset of causal influences change. We then extend our analysis to a broader class of latent post-nonlinear models. Building on these theoretical insights, we develop a flexible method for learning latent causal representations. We demonstrate the effectiveness of our approach on synthetic and semi-synthetic datasets, and further showcase its applicability in a case study on human motion analysis, a complex real-world domain that also highlights the potential to broaden the practical reach of identifiable CRL models.