[SciPy-user] KDE question

[Stefan van der Walt]

On Tue, Nov 13, 2007 at 11:57:20AM -0600, Robert Kern wrote:
> Stefan van der Walt wrote:
> > On Sat, Nov 10, 2007 at 02:08:04AM -0600, Robert Kern wrote:
> >> David Cournapeau wrote:
> >>
> >>> I am not sure I understand exactly the problem, but if the problem is to 
> >>> find a contour level of a Gaussian density, it has a closed form for any 
> >>> dimension.
> >> No, the problem is to find the appropriate contour level of a kernel density
> >> estimate (with Gaussian kernels in this case). Essentially, a mixture of many
> >> Gaussians, not a single one.
> > 
> > Sounds like the kind of problem that can be solved using marching
> > squares:
> > 
> > http://www.polytech.unice.fr/~lingrand/MarchingCubes/algo.html
> 
> This solves the already-matplotlib-solved problem of drawing the contours given
> a level. That still leaves finding the correct level. Or am I underestimating
> the potential to reformulate marching squares to solve the
> integration problem, too?

No, I don't think you are.  As for the line-search, since the
different components of the mixture are available, can't we evaluate
the integral (over each component) directly, rather than working with
a grid?

I come from a GMM background, so a question about KDE: is there a
component placed around each datapoint?  It looks that way, since
there are no means calculated anywhere, as with gaussian mixtures.

Cheers
Stéfan