Increasing which parameter tends to regularize a model in ridge regression?

In ridge regression, the regularization term is controlled by the lambda (λ) parameter. This parameter effectively adjusts the amount of penalty applied to the coefficients of the model. By increasing the value of lambda, you impose a stronger constraint on the size of the coefficients, which leads to a more regularized model. Regularization helps to prevent overfitting, especially in cases where the dataset includes many features or when multicollinearity is present among them.

When lambda is large, the model prioritizes minimizing the complexity of the model by shrinking the coefficients towards zero, hence reducing their variance while accepting some bias. This combination of bias and variance is a trade-off in statistical modeling that can lead to better generalization to unseen data.

The other parameters mentioned, such as alpha (α), do not play a direct role in the regularization process specific to ridge regression, and the budget parameter (a) is not a standard term used in this context. Therefore, the primary factor that regularizes a ridge regression model is indeed the lambda (λ) parameter.