Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation
stat.ML, cs.LG
Submitted: 2026-07-08
Updated: 2026-10-27
License: http://creativecommons.org/licenses/by/4.0/
The gist: Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the joint data
Terminology
Abstract
Missing values undermine statistical inference and machine learning pipelines, yet most imputation methods rely on heuristics or restrictive parametric assumptions that ignore the joint data distribution. We recast imputation under missing completely at random (MCAR) as density estimation from masked observations: estimate a distribution whose observed marginals exactly match those in the data. Leveraging positive semi definite (PSD) kernel densities we obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method. The resulting PSD Impute model yields both single and multiple imputations from the same fitted density, enjoys statistical consistency with fast adaptive excess risk beating the curse of dimensionality for very regular probabilities. Preliminary experiments on one synthetic and eleven real world datasets already indicate competitive distributional accuracy compared with popular imputation baselines, suggesting strong practical promise.
Sources
- Imputation for prediction: beware of diminishing returns
- Explicit and recursive estimates of the Lambert W function
- What Is a Good Imputation Under MAR Missingness?
- Finding Global Minima via Kernel Approximations
- Are deep learning models superior for missing data imputation in large surveys? Evidence from an empirical comparison
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