mlsanityData to 14 Oct 2026

Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing

arXiv 2604.13218 ↗First posted 14 Apr 2026stat.ML cs.AI cs.LGcited by 1

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Abstract (arXiv)

Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 41 of its 59 references that are in the map. First posted on arXiv 14 Apr 2026.

Builds on

41 of 59 references.

References · 41

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29 more
  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
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Citing papers per year: 2026: 1.

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  1. 2026Beyond ICA: Identifiability by Symmetry Breakingcited by 0