[SciPy-user] OLS matrix-f(x) = 0 problem (Was: linear regression)

Gael Varoquaux gael.varoquaux@normalesup....
Wed May 27 15:50:50 CDT 2009


I have been fighting a bit with a OLS regression problem (my ignorance in
regression is wide), and a remark by Robert just prompted me to ask the
list:

On Wed, May 27, 2009 at 02:37:14PM -0500, Robert Kern wrote:
> "f(x)=0" models can express covariances between all dimensions of x.

Sorry for asking you about my 'homework', but people seem so
knowledgeable...

I have a multivariate dataset X, and a given sparse, lower triangular,
boolean, matrix T with an empty diagonal. I am interested in finding the
matrix R for which support(R) == support(T), that is the OLS solution to:

Y = np.dot(R, Y)

I seems to me that the problem can be written in terms of a classic OLS
problem, but I have played with it, and couldn't figure it out.

I don't want to implement an optimisation routine of the L2 norm, because
I have a large number of parameters, and the resulting optimisation will
be dead slow.

I am open to any suggestions, or references.

Thanks a lot,

Gaël


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