Kernel Density Estimation by Genetic Algorithm

TL;DR

This paper introduces a genetic algorithm-based data condensation method to improve multivariate kernel density estimation, resulting in a more efficient and potentially more accurate density estimator.

Contribution

It presents a novel genetic algorithm approach for data condensation in kernel density estimation, enhancing estimator performance through evolutionary techniques.

Findings

The proposed method outperforms traditional density estimators in simulations.

Genetic algorithm effectively reduces data size while maintaining density estimation accuracy.

The approach improves computational efficiency of multivariate kernel density estimation.

Abstract

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The subsamples and their constituting data points are regarded as $\it{chromosome}$ and $\it{gene}$, respectively, in the terminology of genetic algorithm. Second, each pair of subsamples breeds two new subsamples, where each data point faces either $\it{crossover}$, $\it{mutation}$, or $\it{reproduction}$ with a certain probability. The dominant subsamples in terms of fitness values are inherited by the next generation. This process is repeated generation by generation and brings the sparse representation of kernel density estimator in its completion. We confirmed from simulation studies that the resulting estimator can perform better than other well-known density estimators.