# Towards Identifiable Representations under Misspecified Structure

arXiv: https://arxiv.org/abs/2609.33273 · HTML: https://mlsanity.com/paper/2609.33273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deep Learning for Person Re-identification: A Survey and Outlook](https://mlsanity.com/paper/2001.04193/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Person Transfer GAN to Bridge Domain Gap for Person Re-Identification](https://mlsanity.com/paper/1711.08565/) (2017)
- [TransReID: Transformer-based Object Re-Identification](https://mlsanity.com/paper/2102.04378/) (2021)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [CLIP-ReID: Exploiting Vision-Language Model for Image Re-Identification without Concrete Text Labels](https://mlsanity.com/paper/2211.13977/) (2022)
- [Domain Adaptation via Prompt Learning](https://mlsanity.com/paper/2202.06687/) (2022)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [AD-CLIP: Adapting Domains in Prompt Space Using CLIP](https://mlsanity.com/paper/2308.05659/) (2023)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [StyleAdv: Meta Style Adversarial Training for Cross-Domain Few-Shot Learning](https://mlsanity.com/paper/2302.09309/) (2023)
- [Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning](https://mlsanity.com/paper/2211.14666/) (2022)
- [Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies](https://mlsanity.com/paper/2401.04890/) (2024)
- [BISCUIT: Causal Representation Learning from Binary Interactions](https://mlsanity.com/paper/2306.09643/) (2023)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Generalizing Nonlinear ICA Beyond Structural Sparsity](https://mlsanity.com/paper/2311.00866/) (2023)
- [Identification of Nonlinear Latent Hierarchical Models](https://mlsanity.com/paper/2306.07916/) (2023)
- [Temporally Disentangled Representation Learning under Unknown Nonstationarity](https://mlsanity.com/paper/2310.18615/) (2023)
- [Interaction Asymmetry: A General Principle for Learning Composable Abstractions](https://mlsanity.com/paper/2411.07784/) (2024)
- [Split to Merge: Unifying Separated Modalities for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2403.06946/) (2024)
- [Causal Representation Learning from Multimodal Biomedical Observations](https://mlsanity.com/paper/2411.06518/) (2024)
- [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)
- [Learning Causal Domain-Invariant Temporal Dynamics for Few-Shot Action Recognition](https://mlsanity.com/paper/2402.12706/) (2024)
- [Nonparametric Factor Analysis and Beyond](https://mlsanity.com/paper/2503.16865/) (2025)

## Abstract (arXiv)

The presence of noise that depends on the latent variables poses a fundamental challenge to identifiability. Existing results rely on conditional independence among the observations given the latent variables. We study a more general misspecified structure, where this conditional factorization does not hold, and establish both precise and approximate identifiability guarantees. We characterize structural misspecification as a perturbed factor analysis problem. For precise identifiability, we establish subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity. When the precise condition is not guaranteed, we derive an approximate subspace-identifiability theorem. Based on these results, we develop an unsupervised variational estimator for recovering latent variables. Experiments demonstrate the effectiveness of the proposed framework.