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

Question

正如我们所见，caret::train(..., method = "glmnet") 与交叉验证或cv.glmnet() 都实现了可以找到最小化交叉验证错误的lambda.min。最终的最佳拟合模型应该是带有lambda.min 的模型。那么，为什么我们需要为训练过程设置一个lambda 值的网格呢？

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，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：

1. 阿尔法
   • 岭回归（或 alpha = 0）
   • Lasso 回归（或 alpha = 1）
2. λ
   • 对系数的惩罚强度

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），我们可以传递大量 lambda 值来控制惩罚量模型。

train() 足够聪明，每个 alpha 值只能拟合一个模型，并将所有 lambda 值传递到一个以同时拟合。

例子：

# 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)