On the Identifiability of Quantized Factors

TL;DR

This work demonstrates that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism, and introduces this novel form of identifiability, termed quantized factor identifiable, and provides a comprehensive proof of the recovery of the quantized factors.

Abstract

Disentanglement aims to recover meaningful latent ground-truth factors from the observed distribution solely, and is formalized through the theory of identifiability. The identifiability of independent latent factors is proven to be impossible in the unsupervised i.i.d. setting under a general nonlinear map from factors to observations. In this work, however, we demonstrate that it is possible to recover quantized latent factors under a generic nonlinear diffeomorphism. We only assume that the latent factors have independent discontinuities in their density, without requiring the factors to be statistically independent. We introduce this novel form of identifiability, termed quantized factor identifiability, and provide a comprehensive proof of the recovery of the quantized factors.