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(xmis | xobs) 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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BibTeX
@misc{bi2026missing,
title = {{Missing Data Imputation under Manifold Hypothesis}},
author = {Zelong Bi and Amuchechukwu Ibenegbu and Sarat Moka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.03641},
eprint = {2607.03641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03641},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Missing Data Imputation under Manifold Hypothesis
AU - Zelong Bi
AU - Amuchechukwu Ibenegbu
AU - Sarat Moka
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2607.03641
UR - https://arxiv.org/abs/2607.03641
AB - 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(x_mis | x_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.
ER -