# Regularization $L_1$ norm and $L_2$ norm empirical study

There are many methods to perform regularization -- $L_0$, $L_1$, and $L_2$ norm based regularization for example. According to Friedman Hastie & Tibsharani, the best regularizer depends on the problem: namely the nature of the true target function, the particular basis used, signal-to-noise ratio, and sample size.

Is there any empirical research comparing methods and performance of various regularization methods?

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All three authors are at Stanford. Why not just ask one of them directly. Rob Tibshirani is very approachable and so is Jerry Friedman. Friedman did a lot of original research in regularized regression. So he may be the better choice. –  Michael Chernick May 15 '12 at 22:10
You will probably agree this is not really an answer to the question at hand :-) Perhaps you have an opinion on the use of L1 vs. L2 penalty in particular studies you are aware of or you were involved in? –  chl May 15 '12 at 22:37
Of course I can't say that I gave him the answer. But directing him to the best person to answer the question seems like more than just an ordinary comment that usually attempts to clarify. I often wonder why people always ask their questions here when they could go right to the source. I am almost sure that Friedman can answer it and it makes so much sense to go to the source especially when it is a question about something written in their book. I could go to the source get the answer and then present it here. –  Michael Chernick May 16 '12 at 1:25
(continued) Then I would get credit but not help the person anymore than I would by referring him to the source. This is much like some questions where it is easy to google for the answer. I do it and get credit or the OP could do it himself and be less dependent on us. A good thing I think although probably many members here would disagree. –  Michael Chernick May 16 '12 at 1:25
People are intimidated by the source's status as an authority, assume the source is far too busy to deal with their (in their opinion) minor and unimportant question, are afraid of getting a rude "why are you bothering me with this?" answer... It's much easier to go to the source if you, too, are a source, perhaps for other stuff, in the field. –  jbowman May 16 '12 at 1:32