# Measurement Dependence Inducing Latent Causal Models

arXiv: https://arxiv.org/abs/1910.08778 · HTML: https://mlsanity.com/paper/1910.08778/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2019.

## Built on by (most cited first, 14 of 14)

- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations](https://mlsanity.com/paper/2106.03480/) (2021)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)
- [Neuro-Causal Factor Analysis](https://mlsanity.com/paper/2305.19802/) (2023)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering](https://mlsanity.com/paper/2501.11622/) (2025)
- [On Theoretical Identifiability of Discrete Latent Causal Graphical Models](https://mlsanity.com/paper/2505.18410/) (2025)
- [Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models](https://mlsanity.com/paper/2609.24241/) (2026)
- [Identification of Nonlinear and Dependent Latent Factor Structure through Clique Search](https://mlsanity.com/paper/2609.32926/) (2026)

## Abstract (arXiv)

We consider the task of causal structure learning over measurement dependence inducing latent (MeDIL) causal models. We show that this task can be framed in terms of the graph theoretic problem of finding edge clique covers,resulting in an algorithm for returning minimal MeDIL causal models (minMCMs). This algorithm is non-parametric, requiring no assumptions about linearity or Gaussianity. Furthermore, despite rather weak assumptions aboutthe class of MeDIL causal models, we show that minimality in minMCMs implies some rather specific and interesting properties. By establishing MeDIL causal models as a semantics for edge clique covers, we also provide a starting point for future work further connecting causal structure learning to developments in graph theory and network science.