GaussianKDEs.jl: Gaussian Kernel Density Estimators in Julia

Why GaussianKDEs.jl and not KernelDensity.jl? If you want a one-dimensional KDE, it is probably best to use KernelDensity.jl (though GaussianKDEs.jl also has 1D KDEs). However, if you want a multi-dimensional KDE, then KernelDensity.jl is limited to at most 2D, and even in 2D uses axis-aligned kernels to estimate the density; this package can construct KDEs in arbitrary dimension with an arbitrary covariance in the kernel. (In fact, this package constructs densities that are affine invariant, in that the density constructed from some set of points will be a simple Jacobian transformation of the density constructed by any arbitrary shift-and-scale of the same set of points.)

GaussianKDEs.jl has some other features that could be attractive:

• It presents a unified interface for both 1D and multi-dimensional KDEs.
• It allows control over the kernel bandwidth in all dimensions, and includes methods to optimize the bandwidth over a set of test points.
• It implements a BoundedKDE type for 1D KDEs on bounded domains.
• Gaussian KDEs are a proper ContinuousUnivariateDistribution and ContinuousMultivariateDistribution, so they can be used with Distributions.jl methods.

using Pkg
Pkg.add("https://github.com/farr/GaussianKDEs.jl.git")

using Distributions
using GaussianKDEs

k1 = KDE(randn(1024))
pdf(k1, 0) # Should be close to 1/sqrt(2*pi), the PDF for a unit-normal at the origin

npts = 1024
ndim = 4
k4 = KDE(randn(ndim, npts))
pdf(k4, zeros(ndim)) # Should be close to 1/(2*pi)^(ndim/2), the PDF for a unit-normal at the origin

ntest = 128
pts = randn(ndim, npts)
test_pts = randn(ndim, ntest)
k4_opt = bw_opt_kde(pts, test_pts) # Optimal bandwidth for likelihood of the test points.
pdf(k4_opt, zeros(ndim)) # Should be close to 1/(2*pi)^(ndim/2), the PDF for a unit-normal at the origin

ku = BoundedKDE(rand(1024), lower=0, upper=1)
pdf(ku, 0.5) # Should be close to 1, the PDF for a uniform distribution on [0,1]
pdf(ku, 0) # Should be close to 1, the PDF for a uniform distribution on [0,1]
almost_uniform = rand(ku, 1024) # Draw from the bounded distribution implied by the KDE.