Voronoi Density Estimator for High-Dimensional Data: Computation, Compactification and Convergence
International Conference on Uncertainty in Artificial Intelligence(2022)
摘要
The Voronoi Density Estimator (VDE) is an established density estimation
technique that adapts to the local geometry of data. However, its applicability
has been so far limited to problems in two and three dimensions. This is
because Voronoi cells rapidly increase in complexity as dimensions grow, making
the necessary explicit computations infeasible. We define a variant of the VDE
deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher
dimensions. We propose computationally efficient algorithms for numerical
approximation of the CVDE and formally prove convergence of the estimated
density to the original one. We implement and empirically validate the CVDE
through a comparison with the Kernel Density Estimator (KDE). Our results
indicate that the CVDE outperforms the KDE on sound and image data.
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关键词
density,compactification,data,high-dimensional
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