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Re: regularization?
Posted:
Feb 22, 2012 3:45 PM


On Feb 16, Martin Brown <newspam...@nezumi.demon.co.uk> wrote: > > What is regularization, in applied math and stats? > > In this context some function of the reconstructed > model that can be used as a constraint on possible > solutions. In effect steering the solution > towards desirable properties based on a priori > knowledge.
So it's a constraint on the solution space, not the domain space?
It it used exclusively for underdetermined systems?
> For instance the sky is everywhere positive is a > rather powerful strong > constraint in astronomical deconvolution programmes.
?
> This has been encoded in various forms such as > maximum entropy sum(log(f)) by Burg or > sum(flog(f)) by Gull & Daniell. You can choose > various other regularising functions which will > introduce different biasses in the final solution. > sum(f^2) or sum(f") for instance.
I don't understand what these (f) things are, or how they enter the calculations.
> Gull demonstrated it nicely in his Kangaroos problem. see > > http://sci.techarchive.net/Archive > /sci.image.processing/200810/msg00099.html
It might be a nice demonstration nicely, but the article is poorly written.
> ISTR The original paper is called Monkeys, > Kangeroos and N. > > > Is it synonymous with optimization? > > I recently heard a speaker refer to it as > > a means of achieving algorithmic > > and noise robustness, but I didn't get it. > > A suitable choice of regularising function can make > an otherwise ill posed problem tractable and/or > have a unique solution.
It's not clear to me, whether the regularizer is applied to the data as a preprocessing step, or as an extra set of equations to be satisfied.
 Rich



