Supervised Machine Learning with a Novel Kernel Density Estimator

Details Supervised Machine Learning with a Novel Kernel Density Estimator Supervised Machine Learning with a Novel Kernel Density Estimator

2007-09-18

arxiv.org/abs/0709.2760v3

Statistics

Machine Learning

The new version includes an additional theorem, Theorem 3

Scientific paper

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.

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