Information geometric causal inference takes on another approach to infer the causal direction in the pairwise setting. It bases itself on the independence between the cause and the causal mechanism: under the strong assumption that X and Y are related by a bijective relation, the cause $P_X$ is independent from the mechanism $P_{Y | X}$ and not in the opposite direction. This approach can also be related to a complexity approach on the mechanisms

University of Michigan - Ann Arbor

Many approaches basing their inference on predefined features use as input of the classifier already known models for pairwise causal discovery in a stacked classifier fashion. 

Examples of used algorithms are the Additive Noise Model (ANM) model or the Information Geometric Causal Inference (IGCI) model. These two models are the most employed, as they represent a decent tradeoff between performance and computational cost. 

Preexisting Pairwise Causal Discovery Algorithms

 Isabelle Guyon, Alexander Statnikov, Berna Bakir Batu (2019)
Cause Effect Pairs in Machine Learning (The Springer Series on Challenges in Machine Learning)
https://www.amazon.com/Effect-Machine-Learning-Springer-Challenges/dp/3030218090

Cause Effect Pairs in Machine Learning

Additive Noise Model is an extension of LiNGAM model to deal with nonlinear mechanism derived by Hoyer et al. 
A bivariate additive noise model (ANM) X → Y is defined as: 
$Y:=f_Y(X) + N_Y$ with $X \perp \! \! \! \perp N_Y$
where $f_Y : \mathbb{R}\rightarrow \mathbb{R}$ is a Borel measurable function.

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