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Fast, smooth and adaptive regression in metric spaces
Samory Kpotufe

Tue Dec 08 07:00 PM -- 11:59 PM (PST) @
It was recently shown that certain nonparametric regressors can escape the curse of dimensionality in the sense that their convergence rates adapt to the intrinsic dimension of data (\cite{BL:65, SK:77}). We prove some stronger results in more general settings. In particular, we consider a regressor which, by combining aspects of both tree-based regression and kernel regression, operates on a general metric space, yields a smooth function, and evaluates in time $O(\log n)$. We derive a tight convergence rate of the form $n^{-2/(2+d)}$ where $d$ is the Assouad dimension of the input space.

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Samory Kpotufe (Princeton University)

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