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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?

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    $\begingroup$ 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. $\endgroup$ – Macro Aug 31 '12 at 13:41
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    $\begingroup$ @Macro, I think that's an answer, and with a couple of links to the literature, this will be a complete sufficient answer ;) $\endgroup$ – StasK Aug 31 '12 at 16:17

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