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Efficient Locally Weighted Polynomial Regression Predictions
 In Proceedings of the 1997 International Machine Learning Conference
"... Locally weighted polynomial regression (LWPR) is a popular instancebased algorithm for learning continuous nonlinear mappings. For more than two or three inputs and for more than a few thousand datapoints the computational expense of predictions is daunting. We discuss drawbacks with previous appr ..."
Abstract

Cited by 79 (11 self)
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Locally weighted polynomial regression (LWPR) is a popular instancebased algorithm for learning continuous nonlinear mappings. For more than two or three inputs and for more than a few thousand datapoints the computational expense of predictions is daunting. We discuss drawbacks with previous approaches to dealing with this problem, and present a new algorithm based on a multiresolution search of a quicklyconstructible augmented kdtree. Without needing to rebuild the tree, we can make fast predictions with arbitrary local weighting functions, arbitrary kernel widths and arbitrary queries. The paper begins with a new, faster, algorithm for exact LWPR predictions. Next we introduce an approximation that achieves up to a twoordersof magnitude speedup with negligible accuracy losses. Increasing a certain approximation parameter achieves greater speedups still, but with a correspondingly larger accuracy degradation. This is nevertheless useful during operations such as the early stages...
E cient Locally Weighted Polynomial Regression Predictions
"... Locally weighted polynomial regression (LWPR) is a popular instancebased algorithm for learning continuous nonlinear mappings. For more than two or three inputs and for more than a few thousand datapoints the computational expense of predictions is daunting. We discuss drawbacks with previous appr ..."
Abstract
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Locally weighted polynomial regression (LWPR) is a popular instancebased algorithm for learning continuous nonlinear mappings. For more than two or three inputs and for more than a few thousand datapoints the computational expense of predictions is daunting. We discuss drawbacks with previous approaches to dealing with this problem, and present a new algorithm based on a multiresolution search of a quicklyconstructible augmented kdtree. Without needing to rebuild the tree, we can make fast predictions with arbitrary local weighting functions, arbitrary kernel widths and arbitrary queries. The paper begins with a new, faster, algorithm for exact LWPR predictions. Next we introduce an approximation that achieves up to a twoordersofmagnitude speedup with negligible accuracy losses. Increasing a certain approximation parameter achieves greater speedups still, but with a correspondingly larger accuracy degradation. This is nevertheless useful during operations such as the early stages of model selection and locating optima of a tted surface. We also show howthe approximations can permit realtime queryspeci c optimization of the kernel width. We conclude with a brief discussion of potential extensions for tractable instancebased learning on datasets that are too large to t in a computer's main memory.