# Relationship between regularized least squares and MLE

We know that the least square method is equivalent to the MLE for Gaussian distributed errors. What is the relationship (if any) between regularized (Tichonov regularization) least squares and MLE?

• Tikhonov regularized regression (a.k.a. ridge regression) does not map onto a maximum likelihood problem directly - it's a penalized least squares problem. In Bayesian statistics, ridge regression is equivalent to maximizing the ordinary Gaussian likelihood with a Guassian prior on the $\beta$'s. – Macro Aug 31 '12 at 13:41
• @Macro, I think that's an answer, and with a couple of links to the literature, this will be a complete sufficient answer ;) – StasK Aug 31 '12 at 16:17