Theory and Evaluation Metrics for Learning Disentangled Representations

TL;DR

This paper provides a formal framework for understanding disentangled representations, introduces evaluation metrics based on information theory, and demonstrates their effectiveness in comparing different models.

Contribution

It defines precise semantics for disentangled representations and proposes robust, information-theoretic metrics for their evaluation, enabling fair comparison of methods.

Findings

Metrics accurately characterize learned representations

Disentanglement metrics align with qualitative visual assessments

New properties of VAE-based methods are empirically uncovered

Abstract

We make two theoretical contributions to disentanglement learning by (a) defining precise semantics of disentangled representations, and (b) establishing robust metrics for evaluation. First, we characterize the concept "disentangled representations" used in supervised and unsupervised methods along three dimensions-informativeness, separability and interpretability - which can be expressed and quantified explicitly using information-theoretic constructs. This helps explain the behaviors of several well-known disentanglement learning models. We then propose robust metrics for measuring informativeness, separability and interpretability. Through a comprehensive suite of experiments, we show that our metrics correctly characterize the representations learned by different methods and are consistent with qualitative (visual) results. Thus, the metrics allow disentanglement learning methods to be compared on a fair ground. We also empirically uncovered new interesting properties of VAE-based methods and interpreted them with our formulation. These findings are promising and hopefully will encourage the design of more theoretically driven models for learning disentangled representations.