Request/Interest Empirical Distribution type similar to DiscreteNonParametric

[davibarreira]

I'm opening this issue to see if the maintainers of this package are interested in a implementation of a Empirical Distribution type, similar to DiscreteNonParametric, but allowing the support to be multidimensional. I saw that there was a very old issue #358 where the user requested this, but there was no follow up.

I can see many situations where having this distribution could be useful. One example is in the package OptimalTransport.jl, where we make use of DiscreteNonParametric for the 1-D cases, but for multidimensional cases we have to use separate variables for the support and the probabilities. Other examples would be for performing sampling or bootstraping in datasets.

If there is interest in this new distribution, I could try implementing it.

[devmotion]

The discussion in https://github.com/alan-turing-institute/MLJBase.jl/issues/504 seems related.

[cscherrer]

If Distributions doesn't work out, we're very interested in more general distributions like this for MeasureTheory.jl

[davibarreira]

I have to take a look at MeasureTheory.jl. I find the project fascinating, but still haven't found an "excuse" to dive into it. But I'd be glad to contribute.

[gdalle]

I toyed with this concept a few months ago, and I still have some leftover code for a MultivariateCategorical, which is almost the same. Ping me if you want it!

[devmotion]

Ideally this should handle more general support types and not only multivariate or univariate variables if we generalize it.