On Pitfalls of Identifiability in Unsupervised Learning. A Note on: "Desiderata for Representation Learning: A Causal Perspective"

TL;DR

This paper discusses potential pitfalls in model identifiability within unsupervised learning, illustrating how certain models can be indistinguishable yet produce different representations, challenging assumptions of recoverability of true generative models.

Contribution

It presents a counterexample based on nonlinear ICA that highlights limitations of existing identifiability results in representation learning from a causal perspective.

Findings

Counterexample shows models can be observationally indistinguishable

Identifiability results may not guarantee true generative model recovery

Implications for designing robust unsupervised learning methods

Abstract

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.