# Nonparametric Factor Analysis and Beyond

arXiv: https://arxiv.org/abs/2503.16865 · HTML: https://mlsanity.com/paper/2503.16865/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (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)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Generalizing Nonlinear ICA Beyond Structural Sparsity](https://mlsanity.com/paper/2311.00866/) (2023)

## Built on by (most cited first, 4 of 4)

- [Thought Communication in Multiagent Collaboration](https://mlsanity.com/paper/2510.20733/) (2025)
- [Nonparametric Identification of Latent Concepts](https://mlsanity.com/paper/2510.00136/) (2025)
- [Diverse Dictionary Learning](https://mlsanity.com/paper/2604.17568/) (2026)
- [Towards Identifiable Representations under Misspecified Structure](https://mlsanity.com/paper/2609.33273/) (2026)

## Abstract (arXiv)

Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or noiseless regimes. In contrast, we study the more general case where noise can take arbitrary forms, depend on latent variables, and be non-invertibly entangled within a nonlinear function. We propose a general framework for identifying latent variables in the nonparametric noisy settings. We first show that, under suitable conditions, the generative model is identifiable up to certain submanifold indeterminacies even in the presence of non-negligible noise. Furthermore, under the structural or distributional variability conditions, we prove that latent variables of the general nonlinear models are identifiable up to trivial indeterminacies. Based on the proposed theoretical framework, we have also developed corresponding estimation methods and validated them in various synthetic and real-world settings. Interestingly, our estimate of the true GDP growth from alternative measurements suggests more insightful information on the economies than official reports. We expect our framework to provide new insight into how both researchers and practitioners deal with latent variables in real-world scenarios.