Contents
- 1 Can Lambda be negative in ridge regression?
- 2 Do the coefficients using lambda min have more or less bias than the ones using lambda 1se Why would we want to use a model that has more bias rather than one that has less?
- 3 Do you want Ridge to choose a default Lambda sequence?
- 4 When to use a lasso or ridge regression?
Can Lambda be negative in ridge regression?
Short Answer: When lambda is negative, you’re actually overfitting your data. Long Answer: The regularization term (or the penalty term as described by many statisticians) aims to penalize the weights (or the betas as written in the coming Eq.)
Do the coefficients using lambda min have more or less bias than the ones using lambda 1se Why would we want to use a model that has more bias rather than one that has less?
min seem to have more bias than the ones using lambda. 1se. This means we would prefer using lambda. min because we want a higher bias in this case.
What’s the optimal lambda value for ridge regression?
The optimal lambda value comes out to be 0.001 and will be used to build the ridge regression model. We will also create a function for calculating and printing the results, which is done with the eval_results () function in the code below. The next step is to use the predict function to generate predictions on the train and test data.
How to build a ridge regression in R?
To build the ridge regression in r, we use glmnet function from glmnet package in R. Let’s use ridge regression to predict the mileage of the car using mtcars dataset. The glmnet function trains the model multiple times for all the different values of lambda, which we pass as a sequence of vector to the lambda = argument in the glmnet function.
Do you want Ridge to choose a default Lambda sequence?
Yes, you want the lambda that minimizes GCV. MASS’s lm.ridge doesn’t choose a default lambda sequence for you. Look at this question which talks about good default choices for lambda. Also, I’d suggest using cv.glmnet with alpha = 0 (meaning ridge penalty) from glmnet package which will do this cross validation with some good lambdas for you.
When to use a lasso or ridge regression?
To summarize, when lambda is zero, then the lasso model simply gives the least squares fit. Lasso can produce a model involving any number of variables. In contrast, ridge regression will always include all of the variables in the model.