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This research presents a novel, model-based approach to missing data imputation that leverages the manifold hypothesis and mixture variational autoencoders to preserve underlying geometric structures in high-dimensional datasets. By integrating sampling-importance-resampling with joint diffusion models in latent space, the method achieves competitive performance while quantifying uncertainty and enabling efficient on-the-fly inference without retraining.
Missing Data Imputation under Manifold Hypothesis
arXiv:2607.03641v3 Announce Type: replace-cross 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.
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:2607.03641v3 [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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