Kernel embeddings allow for a general and strong representation of the distributions. However, these representation are not specific to the problem of pairwise causal discovery and therefore some patterns might be missed by those.

Therefore, adapting the embeddings to the given distributions and to the task through learning allow the algorithms to automatically distinguish relevant patterns in the distributions.

This paradigm fits with “Deep Learning” or more generally into the “Automatic Machine Learning” concept in which only the data has to be fed to the algorithm with no further domain specific knowledge. This merges representation learning and supervised learning: the algorithms learn their own features based on the given data and task.