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Kernel Density Estimation (KDE) is a nonparametric method for estimating theshape of a density function, given a set of samples from the distribution.Recently, locality-sensitive hashing, originally proposed as a tool for nearestneighbor search, has been shown to enable fast KDE data structures. However,these approaches do not take advantage of the many other advances that havebeen made in algorithms for nearest neighbor algorithms. We present analgorithm called Density Estimation from Approximate Nearest Neighbors (DEANN)where we apply Approximate Nearest Neighbor (ANN) algorithms as a black boxsubroutine to compute an unbiased KDE. The idea is to find points that have alarge contribution to the KDE using ANN, compute their contribution exactly,and approximate the remainder with Random Sampling (RS). We present atheoretical argument that supports the idea that an ANN subroutine can speed upthe evaluation. Furthermore, we provide a C++ implementation with a Pythoninterface that can make use of an arbitrary ANN implementation as a subroutinefor kernel density estimation. We show empirically that our implementationoutperforms state of the art implementations in all high dimensional datasetswe considered, and matches the performance of RS in cases where the ANN yieldno gains in performance.

DEANN: Speeding up Kernel-Density Estimation using Approximate Nearest Neighbor Search