On Pitfalls of Identifiability in Unsupervised Learning. A Note on: "Desiderata for Representation Learning: A Causal Perspective"
This highlights a critical limitation for researchers in causal representation learning, as it challenges the reliability of identifiability claims in the field.
The paper identifies a failure case in the identifiability result from a prior study on unsupervised representation learning, using a counterexample based on nonlinear independent component analysis to show that recovering a ground truth generative model can be impossible.
Model identifiability is a desirable property in the context of unsupervised representation learning. In absence thereof, different models may be observationally indistinguishable while yielding representations that are nontrivially related to one another, thus making the recovery of a ground truth generative model fundamentally impossible, as often shown through suitably constructed counterexamples. In this note, we discuss one such construction, illustrating a potential failure case of an identifiability result presented in "Desiderata for Representation Learning: A Causal Perspective" by Wang & Jordan (2021). The construction is based on the theory of nonlinear independent component analysis. We comment on implications of this and other counterexamples for identifiable representation learning.