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

[josef.pktd at gmail.com]

On Fri, May 13, 2016 at 5:51 PM, Ryan J. Kinnear <ryan at kinnear.ca> 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
https://mail.scipy.org/pipermail/numpy-discussion/2012-February/060921.html


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.

http://www.statsmodels.org/dev/gee.html#dependence-structures
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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