Re: Approximate solution to linear regression
- From: Paige Miller <paige.miller@xxxxxxxxx>
- Date: Tue, 19 Jun 2007 12:44:19 -0700
On Jun 17, 3:46 pm, "vincen...@xxxxxxxxx" <datashap...@xxxxxxxxx>
wrote:
Problem can have 40,000 variables, most of them highly correlated.
More variables than observations in some cases. I came up with an
approach, and my question is
(1) is this an original approach?
(2) more importantly, does it always provide a fairly accurate
solution?
The problem and solution are described athttp://datashaping.com/contest14004.shtml
. The newsgroup can not render the mathematical formatting.
I haven't tried to go through your solution in any detail.
In similar situations, I use Partial Least Squares (PLS) Regression,
which is also an "approximate" method (actually, its a biased
regression) that doesn't care if you have highly correlated X
variables and many more Xs than observations. If you use the maximum
possible number of dimensions in PLS, you will get an OLS solution
without having to invert a matrix.
So, with that in mind, it seems to me your approximate solution is
trying to fit into a niche where there already is a solution, and the
PLS solution has proven useful in zillions of published articles. So
unless you can show that your approximate solution has better
properties than PLS, I don't see much of a need for it.
--
Paige Miller
paige\dot\miller \at\ kodak\dot\com
.
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