Meaning
Statistical constraint methods add a squared magnitude penalty to the loss function of a linear model to prevent overfitting in the presence of correlated variables. The ridge regression penalty shrinks the estimated coefficients toward zero, which reduces the variance of the predictions. It helps in building stable models when the number of features is large relative to the number of samples.
Coefficient Contraction
Regularization prevents the model from assigning too much importance to any single predictor in the data set. The ridge regression penalty forces the coefficients to be smaller by adding their squared values to the cost function. This prevents the model from becoming overly sensitive to noise in the training data.
Bias Tradeoff
The central challenge addressed when choosing the strength of the regularizer is the balance between accuracy and stability. While the ridge regression penalty introduces a small amount of bias into the estimates, it reduces the variance of the model by a larger margin. This exchange often results in a lower mean squared error when the model is applied to new observations from the same distribution.
It ensures that the predictive power of the algorithm remains stable across different samples.
Parameter Selection
Finding the optimal value for the penalty weight requires a process called cross validation.
