Difference between lamda.min and lambda at models minimum SE in cv.glmnet-CodePudding

a <- runif(100)
b <- runif(100)
c <- runif(100)
d <- b   runif(100)/10
e <- a   runif(100)/10

test <- cv.glmnet(cbind(a,b,c), cbind(d,e), family = "mgaussian", relax = TRUE, gamma = c(0.5))
test
test$lambda.min

In this example, calling test directly gives something like:

> test

Call:  cv.glmnet(x = cbind(a, b, c), y = cbind(d, e), gamma = c(0.5),      relax = TRUE, family = "mgaussian") 

Measure: Mean-Squared Error 

    Gamma Index   Lambda Index  Measure        SE Nonzero
min   0.5     1 0.000884    63 0.001603 0.0001329       4
1se   0.5     1 0.014402    33 0.001715 0.0001521       3

It appears that lambda.min should be 0.000884. However, when I call test$lambda.min I get a different number, in this instance 0.0004198282. I'm using glmnet v4.1-4 and R version:

> R.version
               _                           
platform       x86_64-w64-mingw32          
arch           x86_64                      
os             mingw32                     
system         x86_64, mingw32             
status                                     
major          4                           
minor          1.2                         
year           2021                        
month          11                          
day            01                          
svn rev        81115                       
language       R                           
version.string R version 4.1.2 (2021-11-01)
nickname       Bird Hippie

Anyone know why there is a difference?

CodePudding user response：

With relax = TRUE in cv.glmnet, two sets of cross-validation are performed:

the usual one for the relax = FALSE case;
the special one for the relax = TRUE case.

Their results are stored in different places, and there are two methods for print.

Result for relax = FALSE:

print.cv.glmnet(test)

test$lambda.min

Result for relax = TRUE (stored in test$relaxed):

test
#print(test)
#glmnet:::print.cv.relaxed(test)

test$relaxed$lambda.min