Question

What is the purpose to use the leave-one-out cross-validation? Please explain the difference between the ridge regression and LASSO.

Answer 1

Answer:
To understand leave-one-out cross validation first we should understand about cross validation technique.
Cross validation is a model evaluation method which is better than residual evaluation method. In residual evalutaion method it doesn't indicate how well the learner will do when asked to predict based on new data set. On the other hand in Cross Validation method some portion of the data from the training set is removed and model is trained on remaining data, once model is trained its performance is monitored based on its output with the leftout data.

Leave-one-out cross validation is a K-fold cross validation technique which is taken to its logical extereme with K=n, where n is the total data point in the set. The model is trained on all the data except one point and prediction is made for that one point, same is followed for remaining points to calculate the average error which is used to evaluate the model. So by using leave-one-out validation error we can create even better model for prediction even if data set is small, as at any iteration only one is left for prediction remaining is used to train the model.

The main difference between ridge regression and LASSO is both uses two different penalty functions. Ridge uses l2 while LASSO uses l1 penalty function. In rdige regression penalty is sum of square of its coefficients while in LASSO its sum of absolute value of its coefficient.
Also Ridge regression is computationally less intensive compare to LASSO

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