Variational Autoencoders and Nonlinear ICA: A Unifying Framework
This provides a theoretical foundation for disentangled representations in machine learning, addressing a key limitation in generative modeling.
The paper tackles the unidentifiability problem in deep latent-variable models by showing that identification of the true joint distribution over observed and latent variables is possible up to simple transformations, achieving principled disentanglement for a broad family of models, including variational autoencoders and nonlinear ICA.
The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.