Numerical Data Imputation for Multimodal Data Sets: A Probabilistic Nearest-Neighbor Kernel Density Approach
This work addresses data imputation for incomplete multimodal datasets, offering an incremental improvement over existing methods.
The paper tackles the problem of poor imputation in multimodal or complex distributions by introducing the kNN×KDE algorithm, which combines nearest neighbor estimation and Gaussian kernel density estimation, resulting in lower imputation errors and higher likelihood probabilistic estimates compared to current methods.
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 $k$NN$\times$KDE algorithm: a data imputation method combining nearest neighbor estimation ($k$NN) 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