Kernel Density Estimator

Reliable and extremely fast kernel density estimator for one-dimensional data

Description

% Reliable and extremely fast kernel density estimator for one-dimensional data;
% Gaussian kernel is assumed and the bandwidth is chosen automatically;
% Unlike many other implementations, this one is immune to problems
% caused by multimodal densities with widely separated modes (see example). The
% estimation does not deteriorate for multimodal densities, because we never assume
% a parametric model for the data.
% INPUTS:
% data - a vector of data from which the density estimate is constructed;
% n - the number of mesh points used in the uniform discretization of the
% interval [MIN, MAX]; n has to be a power of two; if n is not a power of two, then
% n is rounded up to the next power of two, i.e., n is set to n=2^ceil(log2(n));
% the default value of n is n=2^12;
% MIN, MAX - defines the interval [MIN,MAX] on which the density estimate is constructed;
% the default values of MIN and MAX are:
% MIN=min(data)-Range/10 and MAX=max(data)+Range/10, where Range=max(data)-min(data);
% OUTPUTS:
% bandwidth - the optimal bandwidth (Gaussian kernel assumed);
% density - column vector of length 'n' with the values of the density
% estimate at the grid points;
% xmesh - the grid over which the density estimate is computed;
% Reference: Z. I. Botev, J. F. Grotowski and D. P. Kroese
% "KERNEL DENSITY ESTIMATION VIA DIFFUSION" ,Submitted to the Annals of Statistics, 2009
%
%
% Example:
% data=[randn(100,1);randn(100,1)*2+35 ;randn(100,1)+55];
% [bandwidth,density,xmesh]=kde(data,2^14,min(data)-5,max(data)+5);
% plot(xmesh,density)

% Notes: If you have a more reliable and accurate one-dimensional kernel density
% estimation software, please email me at [e-mail]

• MATLAB release: MATLAB 7.1.0 (R14SP3)
• Other Files: kde.m, ; license.txt

[Dirk Kroese]

Check this out. Much better than the currently available density estimation procedures!

[Tingju Zhu]

Highly recommend this! Very fast and robust.

[Adel Daas]

 

[rao chen]

thanks a lot! it's good.

[Andreas H.]

 

[DI YANG]

Not Bad, But this program is only available for 1d data. But it is still useful some questions . In any way Thanks for sharing.

[Alban Notin]

Thanks for sharing this code. However using Matlab 6.5R13 I had to debug it: inputs arguments I,a2,N not specified for function fixed_point (for example).

[Nate Yoder]

Great code but I believe line 83 should be:
density=idct1d(a_t)/N;
instead of:
density=idct1d(a_t)/R;
in order to get an accurately scaled density function.

[Nate Yoder]

I was incorrect but there does seem to be a scale factor on the density functions

[red]

Yes, the method seems to scale the function so that it becomes a pdf. But my data do not represent a pdf. How can I modify the method so that it works for general (nondensity) estimation?

[Michael Jordan]

 

[Karin Petrini]

 

[Dazhi Jiang]

I think the new version just missed the heading line. Please check it. But still good job. Thank.

[David]

i am using your above code and my data is plotting density values well over 1 (i.e. >500). I looked at your example

% Example:
% data=[randn(100,1);randn(100,1)*2+35 ;randn(100,1)+55];
% [bandwidth,density,xmesh]=kde(data,2^14,min(data)-5,max(data)+5);
% plot(xmesh,density)

but even then, sum(density) = 235.6368, which obviously is greater than 1. It should be 1 if it's a pdf right?

So, does your code generate a pdf? Or is scaled in some other way? If it is not a pdf, do you know how to convert it to a pdf? (do you just normalize by sum(density) ?)

[oluwole ogunkelu]

can someone provide me with hierarchical token bucket(HTB) algorithm used to optimize bandwidth? kinda stucked

[Ange]

Fantastic script - fast and easy to use!