Fast Exact Univariate Kernel Density Estimation

TL;DR

This paper introduces a fast, exact method for univariate kernel density estimation that leverages simple recursions for computational efficiency, outperforming existing approaches in speed and accuracy.

Contribution

It proposes a novel recursive methodology for exact univariate kernel density and derivative estimation, significantly reducing computational complexity.

Findings

Method achieves linear complexity in sample size

Extensive experiments show superior speed and accuracy

Combines exact and approximate methods for enhanced performance

Abstract

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be used to compute density derivative estimates exactly. Given an ordered sample the computational complexity is linear in the sample size. Combining the proposed methodology with existing approximation methods results in extremely fast density estimation. Extensive experimentation documents the effectiveness and efficiency of this approach compared with the existing state-of-the-art.