Another approach to feature construction for pairwise causal discovery is to use distribution embeddings to represent the distribution samples in a latent space as a vector with a fixed number of features.

Unlike computing a custom set of variables, this approach represents each distribution in a latent space and the learning algorithm learns to split this latent space into the different classes. Inference of unseen pairs consist in applying the embedding to the distribution and reporting the label assigned to the region in the latent space corresponding to the image of the sample. One could see this operation as to look for the closest distribution in the training set to the sample and assign its label.

Here are two types of embeddings:

• kernel-based embeddings of the joint distribution
• embeddings of the conditional distributions