cv.glmnet是否使用完整的lambda序列来过度拟合数据？ [英] Is cv.glmnet overfitting the the data by using the full lambda sequence?

问题描述

cv.glmnet 已被大多数研究论文和公司使用。为 glmnet.cr 构建类似的功能，例如 cv.glmnet （类似的程序包，实现套索的连续比率序数回归）我在 cv.glmnet 中遇到了这个问题。

cv.glmnet has been used by most research papers and companies. While building a similar function like cv.glmnet for glmnet.cr (a similar package that implements the lasso for continuation ratio ordinal regression) I came across this problem in cv.glmnet.

`cv.glmnet` first fits the model:



glmnet.object = glmnet(x, y, weights = weights, offset = offset, 
                     lambda = lambda, ...)

在 glmnet 使用完整的数据创建对象，下一步如下：
从拟合的完整模型中提取 lambda

After the glmnet object is created with the complete data, the next step goes as follows: The lambda from the complete model fitted is extracted

lambda = glmnet.object$lambda

现在，他们可以确保折数大于3

Now they make sure number of folds is more than 3

if (nfolds < 3) 
stop("nfolds must be bigger than 3; nfolds=10 recommended")

创建了一个列表来存储交叉验证结果

A list is created to store cross validated results

outlist = as.list(seq(nfolds))

A for循环根据交叉验证理论运行以适合不同的数据部分

A for loop runs to fit different data parts per the theory of cross-validation

  for (i in seq(nfolds)) {
    which = foldid == i
    if (is.matrix(y)) 
      y_sub = y[!which, ]
    else y_sub = y[!which]
    if (is.offset) 
      offset_sub = as.matrix(offset)[!which, ]
    else offset_sub = NULL
#using the lambdas for the complete data 
    outlist[[i]] = glmnet(x[!which, , drop = FALSE], 
                          y_sub, lambda = lambda, offset = offset_sub, 
                          weights = weights[!which], ...)
  }
}

那么会发生什么。将数据拟合为完整数据后，将使用完整数据中的lambda进行交叉验证。有人可以告诉我这怎么可能不是数据过拟合？我们进行交叉验证时，希望模型没有有关数据遗漏部分的信息。但是 cv.glmnet 对此作弊！

So what happens. After fitting the data to the complete data, cross-validation is done, with lambdas from the complete data. Can someone tell me how this can possibly not be data over-fitting?. We in cross-validation want the model to have no information about the left out part of the data. But cv.glmnet cheats on this!

推荐答案

不，这是

cv.glmnet（）确实为lambda序列构建了完整的求解路径。但是您永远不会选择该路径中的最后一个条目。您通常选择 lambda == lambda.1se （或 lambda.min ），如@Fabians所说：

cv.glmnet() does build the entire solution path for the lambda sequence. But you never pick the last entry in that path. You typically pick lambda==lambda.1se (or lambda.min) , as @Fabians said:

lambda==lambda.min : is the lambda-value where cvm is minimized

lambda==lambda.1se : is the lambda-value where (cvm-cvsd)=cvlow is minimized. This is your optimal lambda

请参见 cv.glmnet（）和 coef（...，s ='lambda.1se'）

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