Any plans for a Kernel Density Estimator?

[ndalchau]

The title says it all really. Is anyone considering adding KDE functionality?

[cdrnet]

No concrete plans so far from my side, but I'd certainly accept a pull request.

[waynenilsen]

I'm not sure where this should go but perhaps some variation of below? Got the reference from wikipedia https://en.wikipedia.org/wiki/Kernel_density_estimation

public static double KDE(double at, IList<double> sample, double bandwidth)
{
    return sample.Select(x_i => Normal.PDF(0, bandwidth, at - x_i)).Sum() / sample.Count();
}

Seems to be doing its job

[Bawanglong]

I want this too.
I think it would be nice if one could specify the used kernel, with the Gaussian as a default. Automatic bandwidth selection would also be great (and maybe support for d-dimensional samples).

I'll try to come up with an API and make a proposal for that.

[Bawanglong]

If somebody wants to discuss an API, I opened a PR, see above.

In terms of functionality: So far, it supports 1D samples. What's still missing is some input checking (e.g. samples null or empty), corner-case testing and automatic bandwidth selection.

[cdrnet]

Thanks all for the proposal and first implementation.

I've already pulled in the proposal, but refactored it a bit towards a simpler static and stateless API:

• KernelDensity.Estimate(double x, double bandwidth, IList<double> samples, Func<double, double> kernel)
• KernelDensity.EstimateGaussian(double x, double bandwidth, IList<double> samples)
• ...

I have not included any functionality yet regarding bandwidth rules, but it seems we could support it nicely with overloads in the future.

[cdrnet]

An option would be to add *Func variants returning a lambda on x, i.e. Func<double,double> KernelDensity.EstimateGaussian(double bandwidth, IList<double> samples). We already have this pattern e.g. in Statistics.QuantileFunc.