On Fri, Aug 27, 2010 at 3:27 PM, Sam Birch <sam.m.birch@gmail.com> wrote:
Bandwidth selection is a hotly debated topic, at least in one
dimension, so perhaps not just different methods but tools for
diagnosing bandwidth selection problems would be nice - at the least,
it should be made straightforward to vary the bandwidth (e.g. to plot
the KDE with a range of different bandwidth values).
Well by allowing them to use a custom bandwidth matrix they can vary it themselves, no?
At the other end of the spectrum, for very dense KDEs, on the circle I
found it extremely convenient to use Fourier transforms to carry out
the convolution of kernel with points. In particular, I represented
the KDE in terms of its Fourier coefficients, so that an inverse FFT
immediately gave me the KDE evaluated on a grid (or, with some
fiddling, integrated over the bins of a histogram). I don't know
whether this is a useful optimization for KDEs on the line or in
higher dimensions, since there's the problem of wrapping.
That sounds very interesting. Sorry if I'm being dense (or just wrong, or both), but do you convolve post-FFT or before? If before why does it make it easier?
From the paper it sounded like it's expensive to construct the initial
and also: Do you grid the initial points first ? I think it sounds similar to what Skipper was trying at some point. points, but then much cheaper to evaluate the kde at many points because of the use of the fft for the actual convolution. Josef
-Sam On Fri, Aug 27, 2010 at 2:48 PM, Anne Archibald <aarchiba@physics.mcgill.ca> wrote:
My only experience with KDEs has been on the circle, where there seems to be little or no literature and the constraints are rather different.
On 27 August 2010 14:38, <josef.pktd@gmail.com> wrote:
On Fri, Aug 27, 2010 at 2:17 PM, Sam Birch <sam.m.birch@gmail.com> wrote:
Hi all, I was thinking of renovating the kernel density estimation package (although no promises; I'm leaving for college tomorrow morning!). I was wondering: a) whether anyone had started code in that direction
Mike Crowe wrote code for kernel regression and Skipper started a 1D kernel density estimator in scikits.statsmodels, which cover a larger number of kernels
I don't think I have seen any higher dimensional kernel density estimation in python besides scipy.stats.kde. The Gaussian kde in scipy.stats is targeted to the underlying Fortran code for multivariate normal cdf. It's not clear to me what other n-dimensional kdes would require or whether they would fit well with the current code.
One extension that Robert also mentioned in the past that it would be nice to have adaptive kernels, which I also haven't seen in python yet.
b) what people want in it I was thinking (as an ideal, not necessarily goal): - Support for more than Gaussian kernels (e.g. custom, uniform, Epanechnikov, triangular, quartic, cosine, etc.) - More options for bandwidth selection (custom bandwidth matrices, AMISE optimization, cross-validation, etc.)
definitely yes, I don't think they are even available for 1D yet.
Bandwidth selection is a hotly debated topic, at least in one dimension, so perhaps not just different methods but tools for diagnosing bandwidth selection problems would be nice - at the least, it should be made straightforward to vary the bandwidth (e.g. to plot the KDE with a range of different bandwidth values).
- Assorted conveniences: automatically generate the mesh, limit the kernel's support for speed
Using scipy.spatial to limit the number of neighbors in a bounded support kernel might be a good idea.
Simply using it to find the neighbors that need to be used should speed things up. There may also be some shortcuts for unbounded-support kernels (no point adding a Gaussian a hundred sigma away if there's any points nearby).
At the other end of the spectrum, for very dense KDEs, on the circle I found it extremely convenient to use Fourier transforms to carry out the convolution of kernel with points. In particular, I represented the KDE in terms of its Fourier coefficients, so that an inverse FFT immediately gave me the KDE evaluated on a grid (or, with some fiddling, integrated over the bins of a histogram). I don't know whether this is a useful optimization for KDEs on the line or in higher dimensions, since there's the problem of wrapping.
Anne
(just some thought on the topic)
Josef
So, thoughts anyone? I figure it's better to over-specify and then under-produce, so don't hold back. Thanks, Sam _______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev
_______________________________________________ SciPy-Dev mailing list SciPy-Dev@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-dev