Rethinking Disentanglement Under Dependent Factors of Variation

Abstract

Representation learning enables the discovery and extraction of underlying factors of variation from data. A representation is typically considered disentangled when it isolates these factors in a way that is interpretable to humans. Existing definitions and metrics for disentanglement often assume that the factors of variation are statistically independent. However, this assumption rarely holds in real-world settings, limiting the applicability of such definitions and metrics in real-world applications. In this work, we propose a novel definition of disentanglement grounded in information theory, which remains valid even when the factors are dependent. We show that this definition is equivalent to requiring the representation to consist of minimal and sufficient variables. Based on this formulation, we introduce a method to quantify the degree of disentanglement that remains effective in the presence of statistical dependencies among factors. Through a series of experiments, we demonstrate that our method reliably measures disentanglement in both independent and dependent settings, where existing approaches fail under the latter.