# Numerical Data Imputation for Multimodal Data Sets: A Probabilistic Nearest-Neighbor Kernel Density Approach

arXiv: https://arxiv.org/abs/2306.16906 · HTML: https://mlsanity.com/paper/2306.16906/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 29 Jun 2023.

## Builds on (most cited first, 8 of 8)

- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [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)
- [Analyzing and Improving Representations with the Soft Nearest Neighbor Loss](https://mlsanity.com/paper/1902.01889/) (2019)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [Does imputation matter? Benchmark for predictive models](https://mlsanity.com/paper/2007.02837/) (2020)
- [Missing Data Imputation for Supervised Learning](https://mlsanity.com/paper/1610.09075/) (2016)

## Built on by (most cited first, 3 of 3)

- [Fast Computation of Leave-One-Out Cross-Validation for k-NN Regression](https://mlsanity.com/paper/2405.04919/) (2024)
- [kNNSampler: Stochastic Imputations for Recovering Missing Value Distributions](https://mlsanity.com/paper/2509.08366/) (2025)
- [Precision Adaptive Imputation Network : An Unified Technique for Mixed Datasets](https://mlsanity.com/paper/2501.10667/) (2025)

## Abstract (arXiv)

Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy can create artifacts leading to poor imputation in the presence of multimodal or complex distributions. To tackle this problem, we introduce the kNN×KDE algorithm: a data imputation method combining nearest neighbor estimation (kNN) and density estimation with Gaussian kernels (KDE). We compare our method with previous data imputation methods using artificial and real-world data with different data missing scenarios and various data missing rates, and show that our method can cope with complex original data structure, yields lower data imputation errors, and provides probabilistic estimates with higher likelihood than current methods. We release the code in open-source for the community: https://github.com/DeltaFloflo/knnxkde