为什么需要用 caret::train(..., method = "glmnet") 和 cv.glmnet() 调整 lambda？

Question

正如我们所看到的，caret::train(..., method = "glmnet") 与交叉验证或 cv.glmnet() 都可以找到 lambda.min 来最小化交叉验证错误。最终的最佳拟合模型应该是拟合 lambda.min 的模型。那么，为什么我们需要在训练过程中设置lambda个值的网格？

Answer 1

我们为 glmnet 模型使用自定义调整网格，因为默认调整网格非常小，而且我们可能想要探索更多潜在的 glmnet 模型。

glmnet 能够拟合 2 种不同的惩罚模型，它有 2 个调整参数：

阿尔法
- 岭回归（或 alpha = 0）
- 套索回归（或 alpha = 1）
λ
- 系数惩罚强度

glmnet模型可以一次拟合多个模型（对于单个alpha，lambda的所有值同时拟合），我们可以通过大量的lambda 控制模型中惩罚量的值。

train() 足够聪明，每个 alpha 值只适合一个模型，并将所有 lambda 值同时传递给一个模型。

示例：

# Make a custom tuning grid
tuneGrid <- expand.grid(alpha = 0:1, lambda = seq(0.0001, 1, length = 10))

# Fit a model
model <- train(y ~ ., overfit, method = "glmnet",
  tuneGrid = tuneGrid, trControl = myControl
)


# Sample Output
Warning message: The metric "Accuracy" was not in the result set. ROC will be used instead.
+ Fold01: alpha=0, lambda=1 
- Fold01: alpha=0, lambda=1 
+ Fold01: alpha=1, lambda=1 
- Fold01: alpha=1, lambda=1 
+ Fold02: alpha=0, lambda=1 
- Fold02: alpha=0, lambda=1 
+ Fold02: alpha=1, lambda=1 
- Fold02: alpha=1, lambda=1 
+ Fold03: alpha=0, lambda=1 
- Fold03: alpha=0, lambda=1 
+ Fold03: alpha=1, lambda=1 
- Fold03: alpha=1, lambda=1 
+ Fold04: alpha=0, lambda=1 
- Fold04: alpha=0, lambda=1 
+ Fold04: alpha=1, lambda=1 
- Fold04: alpha=1, lambda=1 
+ Fold05: alpha=0, lambda=1 
- Fold05: alpha=0, lambda=1 
+ Fold05: alpha=1, lambda=1 
- Fold05: alpha=1, lambda=1 
+ Fold06: alpha=0, lambda=1 
- Fold06: alpha=0, lambda=1 
+ Fold06: alpha=1, lambda=1 
- Fold06: alpha=1, lambda=1 
+ Fold07: alpha=0, lambda=1 
- Fold07: alpha=0, lambda=1 
+ Fold07: alpha=1, lambda=1 
- Fold07: alpha=1, lambda=1 
+ Fold08: alpha=0, lambda=1 
- Fold08: alpha=0, lambda=1 
+ Fold08: alpha=1, lambda=1 
- Fold08: alpha=1, lambda=1 
+ Fold09: alpha=0, lambda=1 
- Fold09: alpha=0, lambda=1 
+ Fold09: alpha=1, lambda=1 
- Fold09: alpha=1, lambda=1 
+ Fold10: alpha=0, lambda=1 
- Fold10: alpha=0, lambda=1 
+ Fold10: alpha=1, lambda=1 
- Fold10: alpha=1, lambda=1 
Aggregating results
Selecting tuning parameters
Fitting alpha = 1, lambda = 1 on full training set


# Print model to console
model


# Sample Output
glmnet 

250 samples
200 predictors
  2 classes: 'class1', 'class2' 

No pre-processing
Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 225, 225, 225, 225, 224, 226, ... 
Resampling results across tuning parameters:

  alpha  lambda  ROC        Sens  Spec     
  0      0.0001  0.3877717  0.00  0.9786232
  0      0.1112  0.4352355  0.00  1.0000000
  0      0.2223  0.4546196  0.00  1.0000000
  0      0.3334  0.4589674  0.00  1.0000000
  0      0.4445  0.4718297  0.00  1.0000000
  0      0.5556  0.4762681  0.00  1.0000000
  0      0.6667  0.4783514  0.00  1.0000000
  0      0.7778  0.4826087  0.00  1.0000000
  0      0.8889  0.4869565  0.00  1.0000000
  0      1.0000  0.4869565  0.00  1.0000000
  1      0.0001  0.3368659  0.05  0.9188406
  1      0.1112  0.5000000  0.00  1.0000000
  1      0.2223  0.5000000  0.00  1.0000000
  1      0.3334  0.5000000  0.00  1.0000000
  1      0.4445  0.5000000  0.00  1.0000000
  1      0.5556  0.5000000  0.00  1.0000000
  1      0.6667  0.5000000  0.00  1.0000000
  1      0.7778  0.5000000  0.00  1.0000000
  1      0.8889  0.5000000  0.00  1.0000000
  1      1.0000  0.5000000  0.00  1.0000000

ROC was used to select the optimal model using  the largest value.
The final values used for the model were alpha = 1 and lambda = 1.


# Plot model
plot(model)

为什么需要用 caret::train(..., method = "glmnet") 和 cv.glmnet() 调整 lambda？

Why need to tune lambda with caret::train(..., method = "glmnet") and cv.glmnet()?

r

glmnet