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.

本文讨论了一种可能的未标识结果，说明了非线性独立成分分析理论基础上的建构，并通过适当构造的反例说明了表示学习中的其他反例及其可识别性。

无监督学习中可识别性的陷阱：关于《表示学习的期望：因果透视》的注解

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

Nonnegative matrix factorization (NMF) has become a workhorse for signal and
data analytics, triggered by its model parsimony and interpretability. Perhaps
a bit surprisingly, the understanding to its model identifiability---the major
reason behind the interpretability in many applications such as topic mining
and hyperspectral imaging---had been rather limited until recent years.
Beginning from the 2010s, the identifiability research of NMF has progressed
considerably: Many interesting and important results have been discovered by
the signal processing (SP) and machine learning (ML) communities. NMF
identifiability has a great impact on many aspects in practice, such as
ill-posed formulation avoidance and performance-guaranteed algorithm design. On
the other hand, there is no tutorial paper that introduces NMF from an
identifiability viewpoint. In this paper, we aim at filling this gap by
offering a comprehensive and deep tutorial on model identifiability of NMF as
well as the connections to algorithms and applications. This tutorial will help
researchers and graduate students grasp the essence and insights of NMF,
thereby avoiding typical `pitfalls' that are often times due to unidentifiable
NMF formulations. This paper will also help practitioners pick/design suitable
factorization tools for their own problems.

本文从可识别性的角度出发，详细介绍了非负矩阵分解的模型可识别性及其与算法和应用的联系，帮助研究人员和研究生掌握 NMF 的本质和洞见，避免由于无法识别的 NMF 公式导致的典型‘陷阱’。同时，本文也帮助实践者选择 / 设计适合其问题的分解工具。