# Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation

arXiv: https://arxiv.org/abs/2607.07767 · HTML: https://mlsanity.com/paper/2607.07767/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Finding Global Minima via Kernel Approximations](https://mlsanity.com/paper/2012.11978/) (2020)
- [PSD Representations for Effective Probability Models](https://mlsanity.com/paper/2106.16116/) (2021)
- [Multiple Imputation: A Review of Practical and Theoretical Findings](https://mlsanity.com/paper/1801.04058/) (2018)
- [Imputation for prediction: beware of diminishing returns](https://mlsanity.com/paper/2407.19804/) (2024)
- [Are deep learning models superior for missing data imputation in large surveys? Evidence from an empirical comparison](https://mlsanity.com/paper/2103.09316/) (2021)
- [Imputation Scores](https://mlsanity.com/paper/2106.03742/) (2021)
- [Second order conditions to decompose smooth functions as sums of squares](https://mlsanity.com/paper/2202.13729/) (2022)

## Abstract (arXiv)

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.