SD-KDE: Score-Debiased Kernel Density Estimation
This work addresses bias reduction in density estimation for statistical modeling, but it appears incremental as it builds on existing KDE methods with score-based corrections.
The paper tackles the problem of bias in kernel density estimation by proposing SD-KDE, a method that uses an estimated score function to adjust data points and modify bandwidth, resulting in significant reduction in mean integrated squared error compared to standard Silverman KDE in synthetic and MNIST experiments.
We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a specific choice of step size, followed by standard KDE with a modified bandwidth. The step size and modified bandwidth are chosen to remove the leading order bias in the KDE. Our experiments on synthetic tasks in 1D, 2D and on MNIST, demonstrate that our proposed SD-KDE method significantly reduces the mean integrated squared error compared to the standard Silverman KDE, even with noisy estimates in the score function. These results underscore the potential of integrating score-based corrections into nonparametric density estimation.