Add p-Wasserstein distance

[Sh4pe]

This PR adds the p-Wasserstein distance (a.k.a. Earth Mover Distance). Calculating the p-Wasserstein entails solving a linear program. This is done using JuMP.jl with the Cbc.jl optimizer.

Fixes #37

[johnnychen94]

I would say the main issue of introducing this PR is its huge dependency. You know, at present this package is quite small

julia> @time using Distances
  0.078969 seconds (52.74 k allocations: 3.509 MiB)

Probably this package isn't the best place to put the codes to

[Sh4pe]

I would say the main issue of introducing this PR is its huge dependency. You know, at present this package is quite small

julia> @time using Distances
  0.078969 seconds (52.74 k allocations: 3.509 MiB)

Probably this package isn't the best place to put the codes to

Yes, this PR introduces a lot of dependencies. But since you need to solve a (possibly large) linear program in order to calculate the Wasserstein distance, you need to introduce at least some dependencies (granted that you don't want to re-implement a linear program solver on your own)...

So what do you think would be a better place for the code?

And what do others think?

[Sh4pe]

Another implementation (though solved quite differently) is in #159. Don't really know about the implementation there though.

[devmotion]

FYI: https://github.com/JuliaOptimalTransport/OptimalTransport.jl contains specialized implementations for the 1D solution, both for discrete and continuous distributions, but also a pure Julia implementation for solving the optimal transport problem with discrete measures in arbitrary dimensions (and soon there will be also a specialized implementation for multivariate normal distributions). We just added wasserstein as an interface for computing the p-Wasserstein distance.

[nalimilan]

Adding JuMP as a dependency to Distances.jl would certainly be a problem. As noted at #159 (comment), the 1D Wasserstein distance has a closed form solution, and Distances.jl only includes 1D distances, so we should use that.

[devmotion]

We started splitting OptimalTransport.jl into smaller subpackages, the Wasserstein distances, based on MOI in the general case and including special cases as 1D and e.g. Gaussian distributions, are moved to https://github.com/JuliaOptimalTransport/ExactOptimalTransport.jl.