Gradient Weights help Nonparametric Regressors

author: Samory Kpotufe, Department of Operations Research and Financial Engineering, Princeton University
published: Jan. 16, 2013,   recorded: December 2012,   views: 3336


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In regression problems over real d, 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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