Variational Weighting for Kernel Density Ratios
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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.
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6 of 51 references.
References · 6
- 2017On Calibration of Modern Neural Networkscited by 4,960
- 2018MINE: Mutual Information Neural Estimationcited by 683
- 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
- 2014Nonparametric Estimation of Renyi Divergence and Friendscited by 8
- 2022Local Metric Learning for Off-Policy Evaluation in Contextual Bandits with Continuous Actionscited by 6
- 2014Influence Functions for Machine Learning: Nonparametric Estimators for Entropies, Divergences and Mutual Informationscited by 5
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