Variational Autoencoders and Nonlinear ICA: A Unifying Framework

TL;DR

This paper unifies variational autoencoders and nonlinear ICA, demonstrating that under certain conditions, the true joint distribution over observed and latent variables can be identified, enabling better disentanglement in deep latent-variable models.

Contribution

It extends nonlinear ICA to deep latent-variable models with observed variables, showing that the true joint distribution can be identified up to simple transformations.

Findings

Identification of the true joint distribution is possible with a factorized prior conditioned on observed variables.

The framework extends nonlinear ICA to noisy, undercomplete, or discrete observations.

Includes identifiable flow-based generative models as a special case.

Abstract

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.