Research map / Learning theory and algorithms / Kernels and regression theory
Non-Asymptotic Uniform Rates of Consistency for k-NN Regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| apply finite-sample sup-norm analysis to k-NN regression for α-Hölder functions | k-NN regression · α-Hölder functions in D dimensions | sup-norm estimation rate: ˜O(n^{-α/(2α + D)}) | Helped |
| use unmodified k-NN regression on data supported by a lower-dimensional manifold | k-NN regression · α-Hölder functions on a d-dimensional manifold | sup-norm estimation rate: ˜O(n^{-α/(2α + d)}) | Helped |
| estimate level sets from k-NN regression values on sample points, with threshold λ - ε | k-NN level-set estimator · Level set L_f(λ) | Hausdorff recovery rate: ˜O(n^{-1/(2β + D)}) | Helped |
| apply the same level-set estimator on a lower-dimensional manifold | k-NN level-set estimator · Level set L_f(λ) on a d-dimensional manifold | Hausdorff recovery rate: ˜O(n^{-1/(2β + d)}) | Helped |
| estimate the maximizer by selecting the sample point with highest k-NN regression value | k-NN regression · Unique global maximum in D dimensions | distance to maximum: ˜O(n^{-1/(4+D)}) | Helped |
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