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.

This paper proposes an approach to estimate causal relationships between two variables X and Y when properties of the mechanism changes across the dataset. The authors propose and extension of the non-linear additive noise model [Hoyer et al. 2009] to the case of a mixture of a finite number of non-linear additive noise models, coined Additive Noise Model- Mixture Model (ANM-MM). The authors propose a theoretical identifiability result based on the proof of [Hoyer et al. 2009], then provide an estimation algorithm based on Gaussian Process Partially Observable Models (GPPOM), introduced as a generalization of Gaussian Process Latent Variable Models (GPLVM). Comparison of the approach to baseline for causal inference and clustering are provided on real and simulated data. The problem addressed in this paper is definitively interesting. While some of the experimental results are promising, theoretical and empirical provide a limited understanding of the approach, which is rather complex, and in particular of its strength and limitations.

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.