Questions on the Generalized Tikhonov Regularization

1. What would you use a Tikhonov regularization for?
2. How do you choose Tikhonov regularization parameter?
3. How is the optimal value of the regularization parameter determined?

What would you use a Tikhonov regularization for?

Also known as Tikhonov regularization, named for Andrey Tikhonov, it is a method of regularization of ill-posed problems. It is particularly useful to mitigate the problem of multicollinearity in linear regression, which commonly occurs in models with large numbers of parameters.

How do you choose Tikhonov regularization parameter?

Given a function , an estimate of the noise level, and a positive parameter , choose the regularization parameter such that(2) d ( α ) = b δ for some parameter b > b 0 . If the solution does not exist, then choose α ( δ ) = 0 ; if this equation has many solutions, choose the smallest solution.

How is the optimal value of the regularization parameter determined?

According to the theoretical analysis of QFM, the optimal regularization parameter can be determined effectively through the values of the QF corresponding to different regularization parameters.