Gradient Weights help Nonparametric Regressors
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Abstract
In regression problems over 
the unknown function f often varies more in some coordinates than in others. We show that weighting each coordinate i with the estimated norm of the ith derivative of f is an efficient way to significantly improve the performance of distance-based regressors, e.g. kernel and k-NN regressors. We propose a simple estimator of these derivative norms and prove its consistency. Moreover, the proposed estimator is efficiently learned online.
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