# On Theoretical Identifiability of Discrete Latent Causal Graphical Models

arXiv: https://arxiv.org/abs/2505.18410 · HTML: https://mlsanity.com/paper/2505.18410/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 20 of 20)

- [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)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [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)
- [Measurement Dependence Inducing Latent Causal Models](https://mlsanity.com/paper/1910.08778/) (2019)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [Demystifying amortized causal discovery with transformers](https://mlsanity.com/paper/2405.16924/) (2024)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variables](https://mlsanity.com/paper/2203.04403/) (2022)
- [Learning Discrete Latent Variable Structures with Tensor Rank Conditions](https://mlsanity.com/paper/2406.07020/) (2024)
- [Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learning](https://mlsanity.com/paper/1401.3940/) (2014)
- [Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models](https://mlsanity.com/paper/2104.02143/) (2021)
- [Latent Conjunctive Bayesian Network: Unify Attribute Hierarchy and Bayesian Network for Cognitive Diagnosis](https://mlsanity.com/paper/2301.03665/) (2023)
- [Deep Discrete Encoders: Identifiable Deep Generative Models for Rich Data with Discrete Latent Layers](https://mlsanity.com/paper/2501.01414/) (2025)
- [Identifiability of Latent Class Models with Covariates](https://mlsanity.com/paper/2103.14885/) (2021)

## Abstract (arXiv)

This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure children per latent variable or restrictions on the latent causal graph. Furthermore, it is common for all observed variables to exhibit the same modality. Consequently, the existing identifiability conditions are often too stringent for complex real-world data. We consider a general nonparametric measurement model with arbitrary observed variable types and binary latent variables, and propose a double triangular graphical condition that guarantees identifiability of the entire causal graphical model. The proposed condition significantly relaxes the popular pure children condition. We also establish necessary conditions for identifiability and provide valuable insights into fundamental limits of identifiability. Simulation studies verify that latent structures satisfying our conditions can be accurately estimated from data.