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

**Authors:** Floria Lalande, Kenji Doya  
**arXiv:** [2306.16906](https://arxiv.org/abs/2306.16906)  
**Date:** 2023-06-29  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2306.16906v1/

## Key points

- Numerical data imputation algorithms are commonly used to replace missing values in incomplete datasets.
- Current imputation methods struggle with accurately estimating missing values for multimodal or complex distributions, resulting in poor imputation results.
- The $k$NN$\times$KDE algorithm is proposed as a new data imputation method that combines nearest neighbor estimation ($k$NN) with density estimation using Gaussian kernels (KDE).
- Experiments were conducted using artificial and real-world datasets with different types and rates of missing data to evaluate the effectiveness of the $k$NN$\times$KDE algorithm.
- Results demonstrate that the $k$NN$\times$KDE algorithm can handle complex original data structures and produces lower imputation errors compared to existing methods.
- The approach provides probabilistic estimates with higher likelihoods than current techniques.
- The code for the $k$NN$\times$KDE algorithm has been released as open-source on GitHub for easy access and use by the community (https://github.com/DeltaFloflo/knnxkde).
- The study introduces a novel data imputation method that combines $k$NN and KDE techniques.
- Extensive experiments show that the approach outperforms existing methods in terms of accuracy and likelihood estimation.
- Researchers and practitioners can easily implement and apply the $k$NN$\times$KDE algorithm in their own work for improved outcomes.

## Summary

Numerical data imputation algorithms are commonly used to replace missing values in incomplete datasets. However, current imputation methods often struggle to accurately estimate missing values when dealing with multimodal or complex distributions, leading to poor imputation results. To address this issue, we propose a new data imputation method called the $k$NN$\times$KDE algorithm. This approach combines nearest neighbor estimation ($k$NN) with density estimation using Gaussian kernels (KDE). In order to evaluate the effectiveness of our method, we conducted experiments using both artificial and real-world datasets with different types and rates of missing data. Our results demonstrate that the $k$NN$\times$KDE algorithm is capable of handling complex original data structures and produces lower imputation errors compared to existing methods. Additionally, our approach provides probabilistic estimates with higher likelihoods than current techniques. To facilitate further research and application of our method, we have released the code as open-source on GitHub for the community to access and use (https://github.com/DeltaFloflo/knnxkde). In summary, our study introduces a novel data imputation method that combines $k$NN and KDE techniques. Through extensive experiments, we show that our approach outperforms existing methods in terms of accuracy and likelihood estimation. The availability of our open-source code enables researchers and practitioners to easily implement and apply the $k$NN$\times$KDE algorithm in their own work for improved outcomes.