PSD Impute: New method imputes missing data with distributional fidelity
A convex optimization approach beats the curse of dimensionality for missing data.
Basteri, Ciliberto, and Rudi propose PSD Impute, a distributionally faithful imputation method for missing data under the missing completely at random (MCAR) assumption. Instead of relying on heuristics or parametric assumptions, they recast imputation as density estimation from masked observations: estimate a distribution whose observed marginals exactly match the data. Using positive semi-definite (PSD) kernel densities, the problem becomes a convex empirical risk minimization with closed-form marginals, solvable by a Newton interior point method.
PSD Impute provides both single and multiple imputations from the same fitted density. It enjoys statistical consistency with fast adaptive excess risk, beating the traditional curse of dimensionality for very regular probability distributions. Preliminary experiments on one synthetic and eleven real-world datasets show competitive distributional accuracy compared to popular imputation baselines (e.g., MICE, missForest, GAIN), suggesting strong practical promise for high-dimensional missing data problems.
- Convex formulation: imputation as density estimation with PSD kernels, solved via Newton interior point method.
- Provides both single and multiple imputations from the same fitted density.
- Adaptive excess risk beats curse of dimensionality for regular distributions; tested on 11 real-world datasets.
Why It Matters
This rigorous, statistically consistent method could replace heuristic imputation in ML pipelines, improving downstream inference.