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[SciPy-User] Working with covariance matrices in toeplitz form?

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[SciPy-User] Working with covariance matrices in toeplitz form?

Ryan J. Kinnear
Dear list,

I am working with some Gaussian processes.  I'm interested in whether or
not it's possible to pass around covariance matrices simply as vectors,
taking advantage of the Toeplitz structure.  From what I've read, and
what I've gleaned from looking at the source code my impression is that
the answer to this question is negative.

Has anyone done any work on this?  Could this be a potential feature?

Regards,

-Ryan
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Re: Working with covariance matrices in toeplitz form?

josef.pktd


On Fri, May 13, 2016 at 5:51 PM, Ryan J. Kinnear <[hidden email]> wrote:
Dear list,

I am working with some Gaussian processes.  I'm interested in whether or not it's possible to pass around covariance matrices simply as vectors, taking advantage of the Toeplitz structure.  From what I've read, and what I've gleaned from looking at the source code my impression is that the answer to this question is negative.

Has anyone done any work on this?  Could this be a potential feature?

Scipy has some linear algebra operations for special matrices, like levinson-durbin in this case. In some cases using a sparse matrix can be efficient.

But, AFAIK, there has been no attempt to provide systematic support for patterned matrices. 

Years ago, there has been some discussion, for example


I also tried several times over the years, but never finished anything usable.
We need patterned covariance matrices in statsmodels, but there are currently no general classes for it. Generalized estimating GEE equations has currently the largest collection and supporting methods, but it's tied into the GEE code.

the list might be incomplete or there may be more in PRs

One interesting feature that's useful is if there is a closed form for the inverse cholesky decomposition, which for example for the AR correlation process is just a banded matrix, or a recursive function.

In statsmodels almost everything is use case and application driven, but it would be great if the "numerical" contributors in scipy could add some "proper" methods.

Josef

 

Regards,

-Ryan
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Re: Working with covariance matrices in toeplitz form?

Sturla Molden-3
In reply to this post by Ryan J. Kinnear
"Ryan J. Kinnear" <[hidden email]> wrote:

> Has anyone done any work on this?  Could this be a potential feature?

I am not sure, but would it possible to do this with some stride magic?
I.e. can the regularity of the Toeplitz matrix be expressed as a set of
strides that maps from a covariance matrix to a vector? In that case you
could use the NumPy function as_strided to achieve this effect.

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