FFT-Based Fast Computation of Multivariate Kernel Estimators with Unconstrained Bandwidth Matrices

TL;DR

This paper introduces a novel FFT-based method for efficiently computing multivariate kernel density estimators with unconstrained bandwidth matrices, overcoming previous limitations to improve accuracy and applicability.

Contribution

It presents a new FFT-based approach that handles unconstrained bandwidth matrices in multivariate KDE, expanding the method's flexibility and effectiveness.

Findings

Enables fast computation with unconstrained bandwidth matrices

Overcomes limitations of previous diagonal-only solutions

Facilitates faster bandwidth selection for KDE

Abstract

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes the fast Fourier transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In this paper we describe the problem and give a satisfactory solution. The proposed solution may be successfully used also in other research problems, for example for the fast computation of the optimal bandwidth for KDE.