  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
