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One major drawback of state-of-the-art artificial intelligence is its lack ofexplainability. One approach to solve the problem is taking causality intoaccount. Causal mechanisms can be described by structural causal models. Inthis work, we propose a method for estimating bivariate structural causalmodels using a combination of normalising flows applied to density estimationand variational Gaussian process regression for post-nonlinear models. Itfacilitates causal discovery, i.e. distinguishing cause and effect, by eitherthe independence of cause and residual or a likelihood ratio test. Our methodwhich estimates post-nonlinear models can better explain a variety ofreal-world cause-effect pairs than a simple additive noise model. Though itremains difficult to exploit this benefit regarding all pairs from theT\"ubingen benchmark database, we demonstrate that combining the additive noisemodel approach with our method significantly enhances causal discovery.

Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flows