  Unsupervised representation learning with variational inference relies
heavily on independence assumptions over latent variables. Causal
representation learning (CRL), however, argues that factors of variation in a
dataset are, in fact, causally related. Allowing latent variables to be
correlated, as a consequence of causal relationships, is more realistic and
generalisable. So far, provably identifiable methods rely on: auxiliary
information, weak labels, and interventional or even counterfactual data.
Inspired by causal discovery with functional causal models, we propose a fully
unsupervised representation learning method that considers a data generation
process with a latent additive noise model (ANM). We encourage the latent space
to follow a causal ordering via loss function based on the Hessian of the
latent distribution.
