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note for triangulation schemes
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szcf-weiya committed Mar 19, 2020
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局部回归的主流实现采用 **三角化方案 (triangulation schemes)** 来降低代价,如 S-PLUS 和 R 中的 `loess` 函数,以及 `locfit` 过程(Loader, 1999[^1]).他们在认真选出的 $M$ 个点处精确拟合,代价为 $O(N(M))$,然后采用 blending 技巧来插值拟合其它点(每次赋值代价为 $O(M)$).

!!! note "weiya 注:triangulation schemes"
[Loader (1999)](https://link.springer.com/book/10.1007/b98858)介绍道,在 `locfit` 中,参数 evaluation structure `ev = "phull"` 表示采取三角化方案,而在[最新的 R package](https://cran.r-project.org/web/packages/locfit/locfit.pdf) 中,其 `ev` 可选参数不再包括 `phull`. 或许现在三角化方案不算主流实现?

[^1]: Loader, C. (1999). Local Regression and Likelihood, Springer, New York.

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