# Variational Weighting for Kernel Density Ratios

arXiv: https://arxiv.org/abs/2311.03001 · HTML: https://mlsanity.com/paper/2311.03001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Nonparametric Estimation of Renyi Divergence and Friends](https://mlsanity.com/paper/1402.2966/) (2014)
- [Local Metric Learning for Off-Policy Evaluation in Contextual Bandits with Continuous Actions](https://mlsanity.com/paper/2210.13373/) (2022)
- [Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informations](https://mlsanity.com/paper/1411.4342/) (2014)

## Abstract (arXiv)

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.