Computer Science > Machine Learning
[Submitted on 28 Jun 2023 (v1), last revised 12 Mar 2024 (this version, v3)]
Title:On the Identifiability of Quantized Factors
View PDFAbstract: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.
Submission history
From: Vitoria Barin Pacela [view email][v1] Wed, 28 Jun 2023 16:10:01 UTC (1,396 KB)
[v2] Tue, 5 Dec 2023 16:46:11 UTC (2,952 KB)
[v3] Tue, 12 Mar 2024 20:04:04 UTC (2,940 KB)
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