mlsanityData to 14 Oct 2026

Towards Identifiable Representations under Misspecified Structure

arXiv 2609.33273 ↗First posted 27 Sep 2026cs.LGcited by 0

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Abstract (arXiv)

The presence of noise that depends on the latent variables poses a fundamental challenge to identifiability. Existing results rely on conditional independence among the observations given the latent variables. We study a more general misspecified structure, where this conditional factorization does not hold, and establish both precise and approximate identifiability guarantees. We characterize structural misspecification as a perturbed factor analysis problem. For precise identifiability, we establish subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity. When the precise condition is not guaranteed, we derive an approximate subspace-identifiability theorem. Based on these results, we develop an unsupervised variational estimator for recovering latent variables. Experiments demonstrate the effectiveness of the proposed framework.

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References · 33

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21 more
  1. 2023AD-CLIP: Adapting Domains in Prompt Space Using CLIPcited by 62
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  19. 2024Cross-Modal Few-Shot Learning: a Generative Transfer Learning Frameworkcited by 2
  20. 2025Online Time Series Forecasting with Theoretical Guaranteescited by 2
  21. 2026Content-Style Identification via Differential Independencecited by 2

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