Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning
This work addresses a fundamental problem in unsupervised representation learning for machine learning researchers, offering a general theoretical framework that combines and generalizes previous nonlinear ICA models.
The authors tackled the problem of nonlinear independent component analysis (ICA) by proposing a general framework that uses auxiliary variables and generalized contrastive learning to achieve identifiability of latent variables, with comprehensive proofs provided for model identifiability and estimation consistency.
Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other available information. We propose to learn nonlinear ICA by discriminating between true augmented data, or data in which the auxiliary variable has been randomized. This enables the framework to be implemented algorithmically through logistic regression, possibly in a neural network. We provide a comprehensive proof of the identifiability of the model as well as the consistency of our estimation method. The approach not only provides a general theoretical framework combining and generalizing previously proposed nonlinear ICA models and algorithms, but also brings practical advantages.