Determination of The Tikhonov Factor
The optimal regularization parameter is usually unknown and often in practical problems is determined by an ad hoc method. A possible approach relies on the Bayesian interpretation described above. Other approaches include the discrepancy principle, cross-validation, L-curve method, restricted maximum likelihood and unbiased predictive risk estimator. Grace Wahba proved that the optimal parameter, in the sense of leave-one-out cross-validation minimizes:
where is the residual sum of squares and is the effective number of degrees of freedom.
Using the previous SVD decomposition, we can simplify the above expression:
and
Read more about this topic: Tikhonov Regularization
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