Variable Kernel Density Estimation in High-Dimensional Feature Spaces

Estimating the joint probability density function of a dataset is a central task in many machine learning applications. In this work we address the fundamental problem of kernel bandwidth estimation for variable kernel density estimation in high-dimensional feature spaces. We derive a variable kernel bandwidth estimator by minimizing the leave-one-out entropy objective function and show that this estimator is capable of performing estimation in high-dimensional feature spaces with great success. We compare the performance of this estimator to state-of-the art maximumlikelihood estimators on a number of representative high-dimensional machine learning tasks and show that the newly introduced minimum leave-one-out entropy estimator performs optimally on a number of highdimensional datasets considered.

Authors

• Christiaan van der Walt
• Etienne Barnard

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