问题描述
我试图理解predict.loess函数如何能够在原始数据中不存在的点x处计算新的预测值(y_hat).例如(这是一个简单的例子，我知道这种例子显然不需要黄土，但它说明了这一点):
I am attempting to understand how the predict.loess function is able to compute new predicted values (y_hat) at points x that do not exist in the original data. For example (this is a simple example and I realize loess is obviously not needed for an example of this sort but it illustrates the point):
x <- 1:10
y <- x^2
mdl <- loess(y ~ x)
predict(mdl, 1.5)
[1] 2.25
loess回归是通过在每个x处使用多项式来进行的，因此在每个y处都创建了预测的y_hat.但是，由于没有存储系数，因此在这种情况下，模型"只是用于预测每个y_hat(例如，span或degree)的详细信息.当我执行predict(mdl, 1.5)时，predict如何在这个新的x处产生一个值?是否在两个最接近的现有x值及其关联的y_hat之间进行插值?如果是这样，它如何执行此操作的详细信息是什么?
loess regression works by using polynomials at each x and thus it creates a predicted y_hat at each y. However, because there are no coefficients being stored, the "model" in this case is simply the details of what was used to predict each y_hat, for example, the span or degree. When I do predict(mdl, 1.5), how is predict able to produce a value at this new x? Is it interpolating between two nearest existing x values and their associated y_hat? If so, what are the details behind how it is doing this?
我已经在线阅读了cloess文档，但是找不到在何处进行讨论.
I have read the cloess documentation online but am unable to find where it discusses this.
推荐答案
也许您已经使用过print(mdl)命令，或者只是使用了mdl来查看模型mdl包含的内容，但事实并非如此.该模型非常复杂，并且存储了大量参数.
Maybe you have used print(mdl) command or simply mdl to see what the model mdl contains, but this is not the case. The model is really complicated and stores a big number of parameters.
要了解其中的内容，可以使用unlist(mdl)并查看其中的大量参数.
To have an idea what's inside, you may use unlist(mdl) and see the big list of parameters in it.
这是命令手册的一部分，描述了命令的实际工作方式:
This is a part of the manual of the command describing how it really works:
对于默认族，拟合度是(加权)最小二乘.为了 family ="symmetric"的M估计过程的一些迭代 使用Tukey的biweight.请注意，因为初始值是 最小二乘拟合，这不必是非常可靠的拟合.
For the default family, fitting is by (weighted) least squares. For family="symmetric" a few iterations of an M-estimation procedure with Tukey's biweight are used. Be aware that as the initial value is the least-squares fit, this need not be a very resistant fit.
我相信它试图在每个点的附近拟合一个多项式模型(不仅仅是整个集合的一个多项式).但是，邻域并不仅仅意味着一个点之前和之后的一个点，如果我正在实现这样的功能，我会给与点x最接近的点赋予较大的权重，而给远端点赋予较轻的权重，并尝试拟合一个适合最高的总重量.
What I believe is that it tries to fit a polynomial model in the neighborhood of every point (not just a single polynomial for the whole set). But the neighborhood does not mean only one point before and one point after, if I was implementing such a function I put a big weight on the nearest points to the point x, and lower weights to distal points, and tried to fit a polynomial that fits the highest total weight.
然后，如果要为其预测高度的给定x'最接近点x，我尝试使用拟合在点x的邻域上的多项式-说P(x)-并将其应用于x'-说P(x')-那将是预测.
Then if the given x' for which height should be predicted is closest to point x, I tried to use the polynomial fitted on the neighborhoods of the point x - say P(x) - and applied it over x' - say P(x') - and that would be the prediction.
如果您正在寻找特殊的东西，请告诉我.
Let me know if you are looking for anything special.
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