# Identification of Nonlinear and Dependent Latent Factor Structure through Clique Search

arXiv: https://arxiv.org/abs/2609.32926 · HTML: https://mlsanity.com/paper/2609.32926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Identifiable Deep Generative Models via Sparse Decoding](https://mlsanity.com/paper/2110.10804/) (2021)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Generalizing Nonlinear ICA Beyond Structural Sparsity](https://mlsanity.com/paper/2311.00866/) (2023)
- [Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clustering](https://mlsanity.com/paper/1704.06977/) (2017)
- [Measurement Dependence Inducing Latent Causal Models](https://mlsanity.com/paper/1910.08778/) (2019)
- [Anchored Causal Inference in the Presence of Measurement Error](https://mlsanity.com/paper/1906.00928/) (2019)
- [Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs](https://mlsanity.com/paper/2203.01471/) (2022)
- [Estimation of oblique structure via penalized likelihood factor analysis](https://mlsanity.com/paper/1302.5475/) (2013)
- [The Correlation Thresholding Algorithm for Exploratory Factor Analysis](https://mlsanity.com/paper/2505.21100/) (2025)

## Abstract (arXiv)

Learning the structure of latent factor models involves two central challenges: (1) estimating the number of latent factors and (2) learning the support of the mapping from latent variables to observed variables. This is especially challenging for nonparametric regimes and nonlinear settings. We propose a method for latent structure learning, based on pairwise dependence measures on the observed variables using a graph-theoretic representation. We show that both the number of latent factors and nonlinear mapping structure can be identified from the distribution of observed variables under mild structural assumptions. Unlike prior work restricted to linear correlations, we establish identifiability and consistency for a general class of dependence measures under nonlinear factor models. This motivates a Dependence Thresholding (DT) algorithm, which jointly estimates the number of latent factors and nonlinear mapping structure from observational data alone. We pair this with a neural network architecture constrained by the nonlinear mapping structure, to recover the nonlinear function. Through simulation studies, we show that the DT algorithm is accurate in practice, even when using flexible methods such as neural networks, and exhibits robustness against violations of its assumptions in high-dimensional settings.