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

Gael Varoquaux gael.varoquaux@normalesup....
Thu May 28 14:37:30 CDT 2009

```On Wed, May 27, 2009 at 06:27:29PM -0400, josef.pktd@gmail.com wrote:
> Sounds like a recursive system of linear (simultaneous) equations with
> linear restrictions to me. If you want an unbiased estimator, then
> going row by row, and solving each linear OLS, linalg.lstsq, would be
> the standard way to go. Substuting the previous estimates of the Y's
> into the next step.

Oups, I realise I forgot to answer.

You are right, this is a way to interpret it, and I was solving the
system as you suggest. What didn't like is that the solution I was
getting was dependant on the order of the variables, but I had forgotten
that the lower triangular matrix was an approximation. The
non-permutation-invariance came from this approximation, not the way I
was solving the system.

Unfortunately, it seems that the solution to the complete problem is
still an open research question (FYI the problem is to find the OLS
solution to "M X = X + e", with M definite positive, and with a given
support.

X's dimension are everywhere between (50, 50) to (300, 500), including