FKreg: A MATLAB toolbox for fast Multivariate Kernel Regression

TL;DR

FKreg is a MATLAB toolbox that enables fast, accurate multivariate kernel regression using NUFFT, significantly reducing computation time and including features like bandwidth selection, local polynomial regression, and heteroscedastic variance estimation.

Contribution

Introduces the first fast multivariate kernel regression toolbox in MATLAB utilizing NUFFT with controllable accuracy and efficient bandwidth selection.

Findings

Achieves ${O}(N+M\log M)$ complexity for multivariate kernel regression.

Demonstrates high accuracy and efficiency through simulations and EEG application.

Provides additional features like local polynomial regression and heteroscedastic variance estimation.

Abstract

Kernel smooth is the most fundamental technique for data density and regression estimation. However, time-consuming is the biggest obstacle for the application that the direct evaluation of kernel smooth for $N$ samples needs ${O}\left( {{N}^{2}} \right)$ operations. People have developed fast smooth algorithms using the idea of binning with FFT. Unfortunately, the accuracy is not controllable, and the implementation for multivariable and its bandwidth selection for the fast method is not available. Hence, we introduce a new MATLAB toolbox for fast multivariate kernel regression with the idea of non-uniform FFT (NUFFT), which implemented the algorithm for $M$ gridding points with ${O}\left( N+M\log M \right)$ complexity and accuracy controllability. The bandwidth selection problem utilizes the Fast Monte-Carlo algorithm to estimate the degree of freedom (DF), saving enormous cross-validation time even better when data share the same grid space for multiple regression. Up to now, this is the first toolbox for fast-binning high-dimensional kernel regression. Moreover, the estimation for local polynomial regression, the conditional variance for the heteroscedastic model, and the complex-valued datasets are also implemented in this toolbox. The performance is demonstrated with simulations and an application on the quantitive EEG.