Missing Data Imputation under Manifold Hypothesis
stat.ML, cs.LG
Submitted: 2026-07-03
Updated: 2026-09-14
Comments: correct errors in Appendix A and in Appendix D, update the author list
License: http://creativecommons.org/licenses/by/4.0/
The gist: The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold.
Terminology
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(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.
Sources
- Auto-Encoding Variational Bayes
- UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
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