Causal Discovery with General Non-Linear Relationships using Non-Linear ICA

By Ricardo Pio Monti, Kun Zhang, Aapo Hyvärinen. 2019

108 citations recorded by the source corpus.

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.

Subfields: Analytical Chemistry, Electrochemistry, Signal Processing

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Citations in the corpus

Learning Neural Causal Models from Unknown Interventions (2019, methodology): “Constraint-based methods [7, 28, 29, 30, 27] infer the DAG by analyzing conditional independences in the data.”
Variational Autoencoders and Nonlinear ICA: A Unifying Framework (2019, background): “Importantly, the linear transformation A can often be resolved by linear ICA methods [10, 22], since the component-wise transformations of the latents are still independent, and typically non-Gaussian.”
Learning Sparse Nonparametric DAGs (2019, methodology): “…additive noise models (Hoyer et al., 2009; Peters et al., 2014; Blöbaum et al., 2018; Mooij et al., 2016), post-nonlinear models (Zhang and Hyvärinen, 2009; Zhang et al., 2016) and general nonlinear SEM (Monti et al., 2019; Goudet et al., 2018; Kalainathan et al., 2018; Sgouritsa et al., 2015).”