Adaptivity to Local Smoothness and Dimension in Kernel Regression

Samory Kpotufe, Vikas Garg

Advances in Neural Information Processing Systems 26 (NIPS 2013)

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."