# Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data

arXiv: https://arxiv.org/abs/2509.04415 · HTML: https://mlsanity.com/paper/2509.04415/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Causal machine learning for single-cell genomics](https://mlsanity.com/paper/2310.14935/) (2023)
- [Optimization-based Causal Estimation from Heterogenous Environments](https://mlsanity.com/paper/2109.11990/) (2021)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations](https://mlsanity.com/paper/2106.03480/) (2021)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [Leveraging directed causal discovery to detect latent common causes](https://mlsanity.com/paper/1910.10174/) (2019)
- [Hierarchical and Density-based Causal Clustering](https://mlsanity.com/paper/2411.01250/) (2024)
- [Causal discovery with endogenous context variables](https://mlsanity.com/paper/2412.04981/) (2024)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [Weakly-supervised causal discovery based on fuzzy knowledge and complex data complementarity](https://mlsanity.com/paper/2405.08699/) (2024)

## Built on by (most cited first, 1 of 1)

- [EDGE: Error Dependency Graph-Guided Multi-Error Attribution in Multi-Agent LLM Systems](https://mlsanity.com/paper/2609.01360/) (2026)

## Abstract (arXiv)

Understanding causal heterogeneity is essential for scientific discovery in domains such as biology and medicine. However, existing methods lack causal awareness, with insufficient modeling of heterogeneity, confounding, and observational constraints, leading to poor interpretability and difficulty distinguishing true causal heterogeneity from spurious associations. We propose an unsupervised framework, HCL (Interpretable Causal Mechanism-Aware Clustering with Adaptive Heterogeneous Causal Structure Learning), that jointly infers latent clusters and their associated causal structures from mixed-type observational data without requiring temporal ordering, environment labels, interventions or other prior knowledge. HCL relaxes the homogeneity and sufficiency assumptions by introducing an equivalent representation that encodes both structural heterogeneity and confounding. It further develops a bi-directional iterative strategy to alternately refine causal clustering and structure learning, along with a self-supervised regularization that balance cross-cluster universality and specificity. Together, these components enable convergence toward interpretable, heterogeneous causal patterns. Theoretically, we show identifiability of heterogeneous causal structures under mild conditions. Empirically, HCL achieves superior performance in both clustering and structure learning tasks, and recovers biologically meaningful mechanisms in real-world single-cell perturbation data, demonstrating its utility for discovering interpretable, mechanism-level causal heterogeneity.