Disentanglement Analysis in Deep Latent Variable Models Matching Aggregate Posterior Distributions

TL;DR

This paper introduces a statistical method to evaluate disentanglement in deep latent variable models, including those where latent factors are not aligned with axes, by matching aggregate posterior distributions.

Contribution

The work proposes a general disentanglement evaluation technique applicable to various DLVMs, overcoming limitations of axis-aligned assumptions in existing metrics.

Findings

Method effectively identifies generative factors in different models.

Demonstrated on two datasets with empirical results.

Applicable to models like AAE and WAE-MMD that do not align latent variables with axes.

Abstract

Deep latent variable models (DLVMs) are designed to learn meaningful representations in an unsupervised manner, such that the hidden explanatory factors are interpretable by independent latent variables (aka disentanglement). The variational autoencoder (VAE) is a popular DLVM widely studied in disentanglement analysis due to the modeling of the posterior distribution using a factorized Gaussian distribution that encourages the alignment of the latent factors with the latent axes. Several metrics have been proposed recently, assuming that the latent variables explaining the variation in data are aligned with the latent axes (cardinal directions). However, there are other DLVMs, such as the AAE and WAE-MMD (matching the aggregate posterior to the prior), where the latent variables might not be aligned with the latent axes. In this work, we propose a statistical method to evaluate disentanglement for any DLVMs in general. The proposed technique discovers the latent vectors representing the generative factors of a dataset that can be different from the cardinal latent axes. We empirically demonstrate the advantage of the method on two datasets.