Reviews: Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Models

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.