[SciPy-User] cholesky

Sebastian Walter sebastian.walter@gmail....
Sun Apr 25 08:26:32 CDT 2010


To be honest I also can't quite follow.
For what exactly do you need the Cholesky decomposition, resp. where
does your correlation matrix come from? And how do you compute the
eigenvalues of the Cholesky decomposition?

best regards,
Sebastian




On Sun, Apr 25, 2010 at 11:47 AM, Gael Varoquaux
<gael.varoquaux@normalesup.org> wrote:
> On Fri, Apr 23, 2010 at 10:15:35AM +0100, alexander baker wrote:
>>    We have computed a decomposition matrix using the cholesky method for a
>>    correlation matrix, some of the eigenvalues are negative and we set those
>>    to zero, the question is how can we estimate the significance of removing
>>    these eigenvalues from the original correlation matrix?
>
> I am not sure what you mean by 'the signification'. A correlation matrix
> with negative eigenvalues is an undefined correlation matrix: it
> corresponds to an impossible signal (you are most probably ending up in
> such a situation because you did not have enough independent data samples
> to estimate the correlation matrix).
>
> The best thing you can do, IMHO, is to regularise the correlation matrix.
> In my experience, the Ledoit-Wolf regularisation works really well:
> www.ledoit.net/honey.pdf
>
> I have some code to apply this regularisation, but it is not terribly
> performant (could probably be improved).
>
> Out of curiosity: in what context are you using these correlation
> matrices? What is your final use case?
>
> HTH,
>
> Gaël
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