Contents
How is the tuning parameter lambda chosen in Lasso?
The tuning parameter lambda is chosen by cross validation. When lambda is small, the result is essentially the least squares estimates. As lambda increases, shrinkage occurs so that variables that are at zero can be thrown away.
When to use k as a parameter in cross validation?
The procedure has a single parameter called k that refers to the number of groups that a given data sample is to be split into. As such, the procedure is often called k-fold cross-validation. When a specific value for k is chosen, it may be used in place of k in the reference to the model, such as k=10 becoming 10-fold cross-validation.
How is the number of possible combinations determined in cross validation?
The number of possible combinations is equal to the number of data points in the original sample or n. Cross Validation is a very useful technique for assessing the effectiveness of your model, particularly in cases where you need to mitigate over-fitting.
When to leave one data point out of cross validation?
Leave One Out Cross Validation (LOOCV): This approach leaves 1 data point out of training data, i.e. if there are n data points in the original sample then, n-1 samples are used to train the model and p points are used as the validation set.
Which is an advantage of the LASSO method?
When lambda is small, the result is essentially the least squares estimates. As lambda increases, shrinkage occurs so that variables that are at zero can be thrown away. So, a major advantage of lasso is that it is a combination of both shrinkage and selection of variables.
What is the difference between Ridge and lasso?
Lasso shrinks the coefficient estimates towards zero and it has the effect of setting variables exactly equal to zero when lambda is large enough while ridge does not. Hence, much like the best subset selection method, lasso performs variable selection. The tuning parameter lambda is chosen by cross validation.
How does Lasso minimize the residual sum of squares?
Lasso minimizes the residual sum of squares plus a shrinkage penalty of lambda multiplied by the sum of absolute values of the coefficients. This model performs variable selection in that it restricts some of the coefficients to be exactly zero. The plot shows how many non-zero variables are in the model at the top.
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.