# Differentiable Causal Discovery For Latent Hierarchical Causal Models

arXiv: https://arxiv.org/abs/2411.19556 · HTML: https://mlsanity.com/paper/2411.19556/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 66 references that are in the map.
- First posted on arXiv 29 Nov 2024.

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

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Identification of Nonlinear Latent Hierarchical Models](https://mlsanity.com/paper/2306.07916/) (2023)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Bayesian Pyramids: Identifiable Multilayer Discrete Latent Structure Models for Discrete Data](https://mlsanity.com/paper/2101.10373/) (2021)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Causal Discovery with Multi-Domain LiNGAM for Latent Factors](https://mlsanity.com/paper/2009.09176/) (2020)

## Built on by (most cited first, 3 of 3)

- [TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning](https://mlsanity.com/paper/2601.21135/) (2026)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)
- [Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models](https://mlsanity.com/paper/2609.24241/) (2026)

## Abstract (arXiv)

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.