Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation
For practitioners dealing with missing data, this provides a principled imputation approach that respects the joint distribution without restrictive assumptions, though preliminary results are only competitive with baselines.
The paper tackles missing data imputation under MCAR by recasting it as density estimation from masked observations using PSD kernel densities. The method yields consistent imputations with competitive distributional accuracy on synthetic and real-world datasets.
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.