CrossValidation using glmnet and very high values of Lambda? I am trying to run crossvalidation (folds=10) using glmnet library on my dataset. My outcome of interest is BMI and predictors include a set of clinical variables. My final goal is to use elastic-net regression to select features and also predict BMI. For crossvalidation, I am using a range of alpha from 0 to 1 using a 0.1 increment. I am using min CVM to decide the values of lambda, with my current code I get extremely high estimates for lambda. Are higher values of lambda acceptable or I am failing to see here? Below is my code snippet.  I appreciate all your help and comments. 

size &lt;- floor(nrow(DataFile) * 0.7)
Train_rows &lt;- sample(rownames(DataFile),size=size,replace=FALSE)
Train_Data &lt;- DataFile[Train_rows,]
Train_bmi &lt;- phenoFile[Train_rows,]$BMI

####### Cross Validation Alpha and Lambda #####

myAlpha &lt;-  seq(0,1,by=0.1)


findAlpha_lambda &lt;- function(iAlpha){
   Train_Data &lt;- as.matrix(Train_Data)
   crossModel &lt;- cv.glmnet(Train_Data,Train_bmi,alpha=iAlpha)
   myLambda &lt;- crossModel$lambda.min
   myCVM &lt;- min(crossModel$cvm)
   title &lt;- paste(iAlpha,myLambda,sep="_")
   return(c(iAlpha,myLambda,myCVM))
}

myFrame &lt;- as.data.frame(do.call(rbind,lapply(myAlpha,findAlpha_lambda)))
colnames(myFrame) &lt;- c('Alpha','Lamda','CVM')
myFrame &lt;- myFrame[order(myFrame$CVM),]
print(myFrame)


     Alpha      Lamda      CVM
1    0.0 50.9839208 54.25337
2    0.1  1.7901432 54.37151
3    0.2  3.1427680 54.75240
4    0.3  2.1949422 57.68935
5    0.4  1.8927376 61.68384
9    0.8  1.2510439 63.69622
6    0.5  1.0933677 64.68333
8    0.7  0.2441112 64.73192
7    0.6  2.2050751 65.01727
11   1.0  1.3860429 65.17181
10   0.9  0.5042962 65.70732
I don‘t think a large lambda is a problem per se. It just means that a lot of regularization is going on (under Ridge). See here:

https://stats.stackexchange.com/questions/212056/ridge-lasso-lambda-greater-than-1

Here is a good tutorial from the authors of glmnet. I suggest you check your approach, i.e by looking at various figures as shown in the tutorial, especially plot(cvfit) might be instructive. Also when you go through the tutorial, you see quite „large“ values of lambda (note that log of lambda is plotted). 

https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html