# Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Models

arXiv: https://arxiv.org/abs/1809.08568 · HTML: https://mlsanity.com/paper/1809.08568/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2018.

## Built on by (most cited first, 9 of 9)

- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Hierarchical and Density-based Causal Clustering](https://mlsanity.com/paper/2411.01250/) (2024)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)
- [CCSL: A Causal Structure Learning Method from Multiple Unknown Environments](https://mlsanity.com/paper/2111.09666/) (2021)
- [Causal Coordinated Concurrent Reinforcement Learning](https://mlsanity.com/paper/2401.18012/) (2024)
- [Seeking the Sufficiency and Necessity Causal Features in Multimodal Representation Learning](https://mlsanity.com/paper/2408.16577/) (2024)
- [Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering](https://mlsanity.com/paper/2501.11622/) (2025)
- [Hybrid Causal Identification and Causal Mechanism Clustering](https://mlsanity.com/paper/2507.21792/) (2025)
- [Root Cause Analysis of Measurement and Mechanistic Anomalies](https://mlsanity.com/paper/2601.23026/) (2026)

## Abstract (arXiv)

The inference of the causal relationship between a pair of observed variables is a fundamental problem in science, and most existing approaches are based on one single causal model. In practice, however, observations are often collected from multiple sources with heterogeneous causal models due to certain uncontrollable factors, which renders causal analysis results obtained by a single model skeptical. In this paper, we generalize the Additive Noise Model (ANM) to a mixture model, which consists of a finite number of ANMs, and provide the condition of its causal identifiability. To conduct model estimation, we propose Gaussian Process Partially Observable Model (GPPOM), and incorporate independence enforcement into it to learn latent parameter associated with each observation. Causal inference and clustering according to the underlying generating mechanisms of the mixture model are addressed in this work. Experiments on synthetic and real data demonstrate the effectiveness of our proposed approach.