New Mixture VAE method imputes missing data using manifold hypothesis
Imputes missing data while preserving underlying geometry with uncertainty quantification.
A new paper by Bi, Ibenegbu, and Moka tackles missing data imputation by leveraging the manifold hypothesis — the idea that high-dimensional data lies near a low-dimensional embedded manifold. Their method uses mixture variational autoencoders (VAEs) to extract this structure, then performs imputation via a sampling-importance-resampling (SIR) procedure to draw from the conditional distribution of missing values given observed ones. This can be further augmented with a joint diffusion model in the latent space.
The approach is model-based, meaning once trained, it can impute new missing patterns on the fly without rerunning the entire pipeline. It quantifies uncertainty in imputations and respects the geometry of the data, achieving competitive results against existing imputation methods. The paper is available on arXiv (2607.03641) and targets both machine learning and statistics audiences.
- Uses mixture VAEs to extract low-dimensional manifold structure from high-dimensional data.
- Imputes missing values via sampling-importance-resampling (SIR) from conditional distributions.
- Supports optional latent diffusion model for improved imputation quality and uncertainty quantification.
Why It Matters
Offers a principled, geometry-aware approach to missing data that saves time and provides uncertainty estimates.