Efficient locally weighted polynomial regression predictions (1997) [74 citations — 11 self]
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@INPROCEEDINGS{Moore97efficientlocally,author = {Andrew W. Moore and Jeff Schneider and Kan Deng},
title = {Efficient locally weighted polynomial regression predictions},
booktitle = {In Proceedings of the 1997 International Machine Learning Conference},
year = {1997},
pages = {236--244},
publisher = {Morgan Kaufmann}
}
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Abstract:
Locally weighted polynomial regression (LWPR) is a popular instance-based algorithm for learning continuous non-linear 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 kd-tree. 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 two-ordersof-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 of model selection and locating optima of a fitted surface. We also show how the approximations can permit real-time query-specific optimization of the kernel width. We conclude with a brief discussion of potential extensions for tractable instance-based learning on datasets that are too large to fit in a computer 's main memory.
