# NIPS Proceedingsβ

## Adaptivity to Local Smoothness and Dimension in Kernel Regression

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### 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."