Supervised Machine Learning with a Novel Kernel Density Estimator

TL;DR

This paper introduces a new kernel density estimator for supervised machine learning that achieves a convergence rate of O(n^-2/3) for the mean square error, independent of data dimensionality.

Contribution

It proposes a novel kernel function enabling faster convergence of the density estimator's MSE, improving efficiency in high-dimensional spaces.

Findings

Pointwise MSE converges at O(n^-2/3) with the new kernel.

Convergence rate is dimension-independent under certain conditions.

Efficient density estimation for supervised learning tasks.

Abstract

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or O(n*log(n)) for constructing a classifier, where n is the number of sampling instances. Concerning design of kernel density estimators, one essential issue is how fast the pointwise mean square error (MSE) and/or the integrated mean square error (IMSE) diminish as the number of sampling instances increases. In this article, it is shown that with the proposed kernel function it is feasible to make the pointwise MSE of the density estimator converge at O(n^-2/3) regardless of the dimension of the vector space, provided that the probability density function at the point of interest meets certain conditions.