Re: Least Absolute Deviation solution of a linear system

[James R. Van Zandt]

"John W. Eaton" <address@hidden> writes:

> On 24-Jan-2009, Ben Abbott wrote:
>
> > Personally, I'd like to have this contribution be included in Octave's  
> > core (optimization).
>
> Is it a core Matlab function?

I think it should be considered at least as much a core function as
ols.

 - The LAD regression method is very well established, having been
   "suggested by Boscovich (1757) and studied by Laplace (1793) even
   before the least squares method developed by Legendre (1805) and
   Gauss (1823)" [1].

 - It offers a significant advantage over least squares for some
   problems: it's robust against outliers.

 - Its usefulness is not restricted to one application area.

 - There is a reliable algorithm (i.e. guaranteed to converge, and
   does not require tuning for a specific problem).  

So, I would like to see a function in Octave that finds the LAD
solution of an overdetermined linear system.  This is not to say my
implementation is particularly efficient.  For example, it may be that
a better routine could be coded based on Li and Arce's work [1], and I
would support its inclusion instead.

              - Jim Van Zandt



[1] Yinbo Li and Gonzalo R. Arce, "A maximum likelihood approach to
least absolute deviation regression", EURASIP Journal on Applied
Signal Processing 2004:12, 1762-1769,
http://www.hindawi.com/getpdf.aspx?doi=10.1155/s1110865704401139.