连续值的m估计 [英] m-estimate for continuous values

问题描述

我正在构建自定义回归树，并希望使用m-estimate进行修剪.

I'm building a custom regression tree and want to use m-estimate for pruning.

有人知道如何计算吗?

http://www.ailab.si/blaz /predavanja/UISP/slides/uisp07-RegTrees.ppt 可能会有所帮助(幻灯片12，Em的外观如何?)

http://www.ailab.si/blaz/predavanja/UISP/slides/uisp07-RegTrees.ppt might help (slide 12, how should Em look like?)

推荐答案

m估计很多.他们全都归结为将您的估计问题重现为最小化问题.如果将平方误差用作要最小化的函数，则只会得到样本均值.如果使用误差的绝对值，则将获得样本中位数.想法是使用在这两者之间折衷的函数，以便获得均值的一些效率和中位数的鲁棒性.

There are a lot of m-estimates. They all boil down to recasting your estimation problem as a minimization problem. If you use squared error as the function you're minimizing, you just get sample mean. If you use absolute value of the error, you get the sample median. The idea is to use a function that is a compromise between these two so that you get some of the efficiency of the mean and some of the robustness of the median.

选择函数后，找到一个m估计仅仅是一个优化问题.因此，您的问题实际上归结为寻找优化软件之一.如果您的优化问题是凸的(并且您可以选择m估计量以使问题是凸的)，那么那里就有很多高质量的软件.

Once you've picked your function, finding an m-estimate is just an optimization problem. So your question really boils down to one of finding optimization software. If your optimization problem is convex (and you can pick your m-estimator so that the problem is convex) then there's a lot of high quality software out there.

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