Variational Weighting for Kernel Density Ratios
This work addresses bias reduction in density estimation for machine learning tasks, but it appears incremental as it builds on existing KDE methods.
The paper tackled bias in kernel density estimation for density ratios by deriving an optimal weight function using variational calculus, resulting in improved estimates of prediction posteriors and information-theoretic measures.
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.