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adaptive kernel density estimation in one-dimension

version (3.72 KB) by Zdravko Botev
fast and reliable adaptive kernel density estimator


Updated 21 Jul 2016

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Fast adaptive kernel density estimation in one-dimension in one m-file;
Provides optimal accuracy/speed trade-off. To increase speed when dealing with "big data",
simply reduce the "gam" parameter; Typically "gam=n^(1/3)", where "n" is the length of data.

% [pdf,grid]=akde1d(X,grid,gam)
X - data as a 'n' by '1' vector;
grid - (optional) mesh over which density is to be computed;
default mesh uses 2^12 points over range of data;
gam - (optional) cost/accuracy trade-off parameter, where gam<n;
default value is gam=ceil(n^(1/3))+20; larger values
result in better accuracy, but reduce speed;
to speedup the code, use smaller "gam";

pdf - the value of the estimated density at 'grid'

data=[exp(randn(10^3,1))]; % log-normal sample
[pdf,grid]=akde1d(data); plot(grid,pdf)

Note: If you need a very fast estimator use my "kde.m" function.
This routine is more adaptive at the expense of speed. Use "gam" to control a speed/accuracy tradeoff.

Kernel density estimation via diffusion
Z. I. Botev, J. F. Grotowski, and D. P. Kroese (2010)
Annals of Statistics, Volume 38, Number 5, pages 2916-2957.

Comments and Ratings (2)

Excellent practical results. I'm curious what is the form of the diffusion equation implemented in the code?

Mladen Dalto

It seams line 42 has an error in default gamma:
gam > n when n < 23
so in that case mu=X(perm(1:gam),:) can not be indexed

MATLAB Release Compatibility
Created with R2016a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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