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2013 NIPS NeurIPS 2013

Adaptivity to Local Smoothness and Dimension in Kernel Regression

Abstract

We present the first result for kernel regression where the procedure adapts locally at a point $x$ to both the unknown local dimension of the metric and the unknown H\{o}lder-continuity of the regression function at $x$. The result holds with high probability simultaneously at all points $x$ in a metric space of unknown structure."

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
🧭 Keyword Pioneer — local smoothness
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Machine Learning, Mathematics & Optimization, Reinforcement Learning, Robotics

Authors

Samory Kpotufe , Vikas Garg

Topics

Machine Learning > Core Methods > Regression Machine Learning > Optimization & Theory > Learning Theory Mathematics & Optimization > Optimization > Continuous Optimization Machine Learning > Optimization & Theory > Statistics Machine Learning > Core Methods > Kernel Methods Mathematics & Optimization > Optimization > Kernel Methods

Keywords

nonparametric regression kernel regression non-parametric regression adaptive regression local smoothness adaptivity dimension adaptation metric space holder continuity adaptive estimation metric dimension
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