# Neuro-Causal Factor Analysis

arXiv: https://arxiv.org/abs/2305.19802 · HTML: https://mlsanity.com/paper/2305.19802/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 121 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 46)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [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)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [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)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Deep Learning of Representations: Looking Forward](https://mlsanity.com/paper/1305.0445/) (2013)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [Visual Causal Feature Learning](https://mlsanity.com/paper/1412.2309/) (2014)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Identifiable Deep Generative Models via Sparse Decoding](https://mlsanity.com/paper/2110.10804/) (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)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Overparameterized Neural Networks Implement Associative Memory](https://mlsanity.com/paper/1909.12362/) (2019)
- [Graphical Normalizing Flows](https://mlsanity.com/paper/2006.02548/) (2020)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)

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

- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)

## Abstract (arXiv)

Factor analysis (FA) is a statistical method for explaining how mutually dependent observed variables can be represented in terms of mutually independent latent factors, and it is widely used in the psychological, biological, and physical sciences. We revisit this classic method from the perspective of recent advances in causal structure learning and deep generative models, introducing a framework for Neuro-Causal Factor Analysis (NCFA). Our approach is fully nonparametric: it learns a directed graph between latent and observed variables, and then fits a deep generative model constrained to respect the Markov factorization of the graph. Empirically, on synthetic and real data, NCFA attains better reconstruction error compared to standard FA and better latent distribution recovery compared to a standard variational autoencoder, all with the advantages of sparser architecture, lower model complexity, and causal interpretability.