# Identifiable Latent Polynomial Causal Models Through the Lens of Change

arXiv: https://arxiv.org/abs/2310.15580 · HTML: https://mlsanity.com/paper/2310.15580/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 24 of 24)

- [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)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [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)
- [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)
- [Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning](https://mlsanity.com/paper/2107.00848/) (2021)
- [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)
- [Pathwise Derivatives Beyond the Reparameterization Trick](https://mlsanity.com/paper/1806.01851/) (2018)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [How Image Degradations Affect Deep CNN-based Face Recognition?](https://mlsanity.com/paper/1608.05246/) (2016)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [Learning Latent Causal Dynamics](https://mlsanity.com/paper/2202.04828/) (2022)
- [Variational Bayesian Dropout with a Hierarchical Prior](https://mlsanity.com/paper/1811.07533/) (2018)

## Built on by (most cited first, 23 of 23)

- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (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)
- [CLAP: Isolating Content from Style through Contrastive Learning with Augmented Prompts](https://mlsanity.com/paper/2311.16445/) (2023)
- [Beyond DAGs: A Latent Partial Causal Model for Multimodal Learning](https://mlsanity.com/paper/2402.06223/) (2024)
- [On the Value of Cross-Modal Misalignment in Multimodal Representation Learning](https://mlsanity.com/paper/2504.10143/) (2025)
- [Language Agents Meet Causality -- Bridging LLMs and Causal World Models](https://mlsanity.com/paper/2410.19923/) (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)
- [Causal Representation Learning from General Environments under Nonparametric Mixing](https://mlsanity.com/paper/2604.23800/) (2026)
- [What Makes a Representation Good for Single-Cell Perturbation Prediction?](https://mlsanity.com/paper/2605.19343/) (2026)
- [Causal Disentanglement and Cross-Modal Alignment for Enhanced Few-Shot Learning](https://mlsanity.com/paper/2508.03102/) (2025)
- [Linear causal disentanglement via higher-order cumulants](https://mlsanity.com/paper/2407.04605/) (2024)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing](https://mlsanity.com/paper/2604.13218/) (2026)
- [Learning Latent Dynamical Causal Processes for Single-Cell Perturbation Prediction](https://mlsanity.com/paper/2605.25581/) (2026)
- [Rethinking State Disentanglement in Causal Reinforcement Learning](https://mlsanity.com/paper/2408.13498/) (2024)
- [Learning Counterfactually Fair Models via Improved Generation with Neural Causal Models](https://mlsanity.com/paper/2502.12796/) (2025)
- [Concept Component Analysis: A Principled Approach for Concept Extraction in LLMs](https://mlsanity.com/paper/2601.20420/) (2026)
- [Boundary Embedding Shaping with Adaptive Contrastive Learning for Graph Structural Disentanglement](https://mlsanity.com/paper/2606.20283/) (2026)
- [Conditionally Identifiable Latent-Environment Modeling for Out-of-Distribution Recommendation](https://mlsanity.com/paper/2608.03647/) (2026)
- [Jigsaw-CRL: Recovering Global Latent Causal Order from Fragmented Multi-Client Interventions](https://mlsanity.com/paper/2608.28991/) (2026)
- [I Act Therefore I Am: When Is JEPA's Action-Conditioning Enough to Learn Causal Mechanisms?](https://mlsanity.com/paper/2609.31161/) (2026)

## Abstract (arXiv)

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments citepliu2022identifying. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.