SD-KDE: Score-Debiased Kernel Density Estimation

Elliot Epstein (Stanford University) · Rajat Vadiraj Dwaraknath (Stanford University) · Thanawat Sornwanee (Stanford University) · John Winnicki (Stanford University) · Jerry Liu (Stanford University)

asymptotic convergence bias reduction debiasing density estimation dimensionality reductionkernel density estimationmean integrated squared errormodified bandwidthnoise robustnessnonparametric methodsscore functionscore-based correctionssd-kdesilverman kdestep sizesynthetic tasks

We propose a 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, improving the asymptotic convergence rate. 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.