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From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: [Math] "LUDecomposition" in "AbstractLeastSquaresOptimizer"
Date Thu, 08 Sep 2011 15:20:35 GMT
Rank revealing Cholesky should be effectively about as good as an eigen
solution.  The pivoting results in non-increasing diagonals and a sharp rank
indicator.  You can do pseudo inverse things with the result as well.

Getting the actual pseudo inverse isn't a bad thing.  I just don't see it as
entirely necessary.

On Thu, Sep 8, 2011 at 7:49 AM, Greg Sterijevski <gsterijevski@gmail.com>wrote:

> Cholesky, in my opinion, is not robust as you have discovered. When it
> encounters a non-psd matrix it gives up. Maybe that is the correct course
> of
> action, but I still think that when you are using the getCovariance to
> estimate the curvature in the neighborhood of a point it would be okay to
> take the generalized inverse and not worry too much about why your matrix
> is
> bordering on non-PSDness... If your optimization stops on that point, that
> is another story and should be flagged.
>
>
>
> > A possibly more robust option here is to use Cholesky decomposition,
> > > which is known to be stable for symmetric positive definite
> > > matrices, which the covariance matrix being inverted here should
> > > be.  The exceptions thrown will be different; but they will give
> > > more specific information about what is wrong with the covariance
> > > matrix.
> >
> > I've tried it with my problem, and it also throws an exception.
> > However, I would like to obtain the covariance matrix anyway, because
> I've
> > no other clue as to what might be wrong.
> > So I think that, at least, users should be able to set the positive
> > definiteness threshold in order to avoid raising an exception.
> >
> >
> >
>

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