Missing Data Imputation under Manifold Hypothesis

• URL: http://arxiv.org/abs/2607.03641v1
• Date: Fri, 03 Jul 2026 23:42:33 GMT
• Title: Missing Data Imputation under Manifold Hypothesis
• Abstract summary: manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold.<n>Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner.<n>We propose a model-based imputation method that enables sampling from ( p(bmx_mathrmmis mid bmx_mathrmobs) ) via a sampling-importance-resampling (SIR) procedure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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