On the Identifiability of Nonlinear ICA with Unconditional Priors

Yujia Zheng, Ignavier Ng, Kun Zhang

TL;DR: In this work, we aim to show the identifiability of nonlinear ICA with unconditional priors under specific conditions.

Abstract: Nonlinear independent component analysis (ICA) aims to recover the underlying marginally independent latent sources from their observable nonlinear mixtures. The identifiability of nonlinear ICA is a major unsolved problem in unsupervised learning. Recent breakthroughs reformulate the standard marginal independence assumption of sources as conditional independence given some auxiliary variables (e.g., class labels) as weak supervision or inductive bias. However, the modified setting might not be applicable in many scenarios that do not have auxiliary variables. We explore an alternative path and consider only assumptions on the mixing process, such as independent influences. We show under these assumptions that the marginally independent latent sources can be identified from the nonlinear mixtures up to a component-wise (linear) transformation and a permutation, thus providing an identifiability result of nonlinear ICA without auxiliary variables. We provide an estimation method and validate the theoretical results experimentally.