Variational Weighting for Kernel Density Ratios

Published: 21 Sept 2023, Last Modified: 15 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Kernel Density Estimation, KL-divergence, Density Ratio
TL;DR: Variational Weighting for Kernel Density Ratios
Abstract: Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias in standard kernel density estimates for density ratios, leading to improved estimates of prediction posteriors and information-theoretic measures. In the process, we shed light on some fundamental aspects of density estimation, particularly from the perspective of algorithms that employ KDEs as their main building blocks.
Submission Number: 7279