Fast, smooth and adaptive regression in metric spaces
نویسنده
چکیده
It was recently shown that certain nonparametric regressors can escape the curse of dimensionality when the intrinsic dimension of data is low ([1, 2]). 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, adapts to intrinsic dimension, operates on general metrics, yields a smooth function, and evaluates in time O(logn). 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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