Least squares regularization is a statistical method used to reduce the impact of overfitting in regression models. It involves adding a penalty term to the loss function to control the complexity of the model and prevent it from fitting too closely to the training data.
Regularization is necessary in least squares regression to prevent overfitting, which occurs when a model fits too closely to the training data and performs poorly on new, unseen data. It helps to balance the bias-variance tradeoff and produces a more generalizable model.
No, least squares regularization does not always have to be iterative. While some regularization techniques, such as ridge regression and lasso regression, involve an iterative process to find the optimal penalty term, other methods, such as elastic net regression, have closed-form solutions that do not require iteration.
Iterative least squares regularization works by updating the model parameters in each iteration based on the gradient of the loss function with respect to the penalty term. This process continues until a stopping criterion is met, such as when the change in the loss function or model parameters falls below a certain threshold.
The benefits of using least squares regularization include improved model performance on new data, reduced overfitting, and better interpretability of the model. It also allows for the inclusion of a large number of features without the risk of overfitting, making it a popular choice for high-dimensional datasets.