# Identifying Weight-Variant Latent Causal Models

arXiv: https://arxiv.org/abs/2208.14153 · HTML: https://mlsanity.com/paper/2208.14153/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 79 references that are in the map.
- First posted on arXiv 30 Aug 2022.

## Builds on (most cited first, 30 of 37)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [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)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [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)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [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)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [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)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Heterogeneous Risk Minimization](https://mlsanity.com/paper/2105.03818/) (2021)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)

## Built on by (most cited first, 30 of 34)

- [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)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [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)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Causal Representation Learning Made Identifiable by Grouping of Observational Variables](https://mlsanity.com/paper/2310.15709/) (2023)
- [Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models](https://mlsanity.com/paper/2402.09236/) (2024)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data?](https://mlsanity.com/paper/2503.08980/) (2025)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [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)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (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)
- [Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Models](https://mlsanity.com/paper/2306.11281/) (2023)
- [What Makes a Representation Good for Single-Cell Perturbation Prediction?](https://mlsanity.com/paper/2605.19343/) (2026)
- [From Invariant Representations to Invariant Data: Provable Robustness to Spurious Correlations via Noisy Counterfactual Matching](https://mlsanity.com/paper/2505.24843/) (2025)
- [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)
- [Learning Latent Dynamical Causal Processes for Single-Cell Perturbation Prediction](https://mlsanity.com/paper/2605.25581/) (2026)
- [Diffusion Based Causal Representation Learning](https://mlsanity.com/paper/2311.05421/) (2023)
- [Rethinking State Disentanglement in Causal Reinforcement Learning](https://mlsanity.com/paper/2408.13498/) (2024)
- [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)

## Abstract (arXiv)

The task of causal representation learning aims to uncover latent higher-level causal variables that affect lower-level observations. Identifying the true latent causal variables from observed data, while allowing instantaneous causal relations among latent variables, remains a challenge, however. To this end, we start with the analysis of three intrinsic indeterminacies in identifying latent variables from observations: transitivity, permutation indeterminacy, and scaling indeterminacy. We find that transitivity acts as a key role in impeding the identifiability of latent causal variables. To address the unidentifiable issue due to transitivity, we introduce a novel identifiability condition where the underlying latent causal model satisfies a linear-Gaussian model, in which the causal coefficients and the distribution of Gaussian noise are modulated by an additional observed variable. Under certain assumptions, including the existence of a reference condition under which latent causal influences vanish, we can show that the latent causal variables can be identified up to trivial permutation and scaling, and that partial identifiability results can still be obtained when this reference condition is violated for a subset of latent variables. Furthermore, based on these theoretical results, we propose a novel method, termed Structural caUsAl Variational autoEncoder (SuaVE), which directly learns causal representations and causal relationships among them, together with the mapping from the latent causal variables to the observed ones. Experimental results on synthetic and real data demonstrate the identifiability and consistency results and the efficacy of SuaVE in learning causal representations.