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Topic: regularization?
Replies: 6   Last Post: Feb 28, 2012 11:16 AM

 Messages: [ Previous | Next ]
 Rich Delaney Posts: 349 Registered: 12/13/04
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.tech-archive.net/Archive
> /sci.image.processing/2008-10/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 pre-processing step,
or as an extra set of equations to be satisfied.

--
Rich

Date Subject Author
2/15/12 Rich Delaney
2/16/12 Martin Brown
2/22/12 Rich Delaney
2/23/12 Martin Brown
2/23/12 Richard Ulrich
2/28/12 aruzinsky
2/28/12 aruzinsky