AAAI Publications, Thirty-First AAAI Conference on Artificial Intelligence

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Variable Kernel Density Estimation in High-Dimensional Feature Spaces
Christiaan Maarten van der Walt, Etienne Barnard

Last modified: 2017-02-13

Abstract


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 maximum-likelihood 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 high-dimensional datasets considered.

Keywords


machine learning; probability density estimation; non-parametric density estimation; kernel bandwidth estimation; kernel density estimation; maximum-likelihood; high-dimensional

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