structural:scholar_edition, linguistic:translation
Tikhonov regularization

In some contexts, a regularized version of the least squares solution may be preferable. Tikhonov regularization (or ridge regression) adds a constraint that ‖ β ‖ 2 2 {\displaystyle \left\|\beta \right\|_{2}^{2}}, the squared ℓ 2 {\displaystyle \ell _{2}} -norm of the parameter vector, is not greater than a given value to the least squares formulation, leading to a constrained minimization problem. This is equivalent to the unconstrained minimization problem where the objective function is the residual sum of squares plus a penalty term α ‖ β ‖ 2 2 {\displaystyle \alpha \left\|\beta \right\|_{2}^{2}} and α {\displaystyle \alpha } is a tuning parameter (this is the Lagrangian form of the constrained minimization problem).

In a Bayesian context, this is equivalent to placing a zero-mean normally distributed prior on the parameter vector.