[Numpy-discussion] warning or error for non-physical multivariate_normal covariance matrices?

Charles R Harris charlesr.harris@gmail....
Tue Sep 15 14:31:21 CDT 2009


On Tue, Sep 15, 2009 at 1:28 PM, Michael Gilbert <
michael.s.gilbert@gmail.com> wrote:

> On Tue, 15 Sep 2009 13:17:43 -0600, Charles R Harris wrote:
> > On Tue, Sep 15, 2009 at 12:57 PM, Michael Gilbert <
> > michael.s.gilbert@gmail.com> wrote:
> >
> > > On Tue, 15 Sep 2009 13:26:23 -0500, Robert Kern wrote:
> > > > On Tue, Sep 15, 2009 at 12:50, Charles R
> > > > Harris<charlesr.harris@gmail.com> wrote:
> > > > >
> > > > >
> > > > > On Tue, Sep 15, 2009 at 11:38 AM, Michael Gilbert
> > > > > <michael.s.gilbert@gmail.com> wrote:
> > > > >>
> > > > >> hi,
> > > > >>
> > > > >> when using numpy.random.multivariate_normal, would it make sense
> to
> > > warn
> > > > >> the user that they have entered a non-physical covariance matrix?
> i
> > > was
> > > > >> recently working on a problem and getting very strange results
> until i
> > > > >> finally realized that i had actually entered a bogus covariance
> > > matrix.
> > > > >>
> > > > >> its easy to determine when this is the case -- its when the
> > > > >> determinant of the covariance matrix is negative.  i.e. the
> > > > >> multivariate normal distribution has det(C)^1/2 as part of the
> > > > >> normalization factor, so when det(C)<0, you end up with an
> imaginary
> > > > >> probability distribution.
> > > > >>
> > > > >
> > > > > Hmm, you mean it isn't implemented using a cholesky decomposition?
> That
> > > > > would (should) throw an error if the covariance isn't symmetric
> > > positive
> > > > > definite.
> > > >
> > > > We use the SVD to do the matrix square root. I believe I was just
> > > > following the older code that I was replacing. I have run into nearly
> > > > degenerate cases where det(C) ~ 0 such that the SVD method gave not
> > > > unreasonable answers, given the circumstances, while the Cholesky
> > > > decomposition gave an error "too soon" in my estimation.
> > >
> > > i just tried a non-symmetric covariance matrix, which, like you
> > > mention is also non-physical.  there were also no errors for this
> > > situation, and the results will obviously be incorrect.
> > >
> > > regardless of the method for determining the matrix square root, it
> > > should be possible to determine whether an error needs to be thrown
> > > based on whether or not the result is imaginary, right?
> > >
> > >
> > The singular values should all be non-negative, if not there is a bug
> > somewhere. Can you post the matrix that has the negative singular values?
> > The symmetry can be checked in various ways. I think some sort of check
> > would be appropriate. Open a ticket.
>
> will do.  where is your tracker at?
>
> Go to www.scipy.org, click on the bug icon, and follow directions.

Chuck
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