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

[Charles R Harris]

On Tue, Sep 15, 2009 at 12:57 PM, Michael Gilbert <
michael.s.gilbert at 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 at gmail.com> wrote:
> > >
> > >
> > > On Tue, Sep 15, 2009 at 11:38 AM, Michael Gilbert
> > > <michael.s.gilbert at 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.

Chuck
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