Missing Data Imputation under Manifold Hypothesis

Abstract:The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold. Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner. The resulting geometric structure naturally introduces local and global relationships among variables, thereby providing a systematic way of imputing missing data. We propose a model-based imputation method that enables sampling from \( p(\bm{x}_{\mathrm{mis}} \mid \bm{x}_{\mathrm{obs}}) \) via a sampling-importance-resampling (SIR) procedure, which can be further augmented with a joint diffusion model in the latent space. Our method imputes missing data while respecting the underlying geometry, achieves competitive performance compared to state-of-the-art procedures, quantifies uncertainty in the imputations, and is model-based, thereby enabling on-the-fly imputation without rerunning the entire procedure.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2607.03641 [stat.ML]

(or arXiv:2607.03641v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.03641 Focus to learn more arXiv-issued DOI via DataCite

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