Wasserstein distance

[matbesancon]

It is not explained why the Wasserstein distance is used, and why no other? Could other divergence metrics be used? Wasserstein seems to appear in the code but not in explanations

[kirui93]

We have not used the Wasserstein distance for numerical calculations. The Wasserstein distance does not take into account the increasing information at successive stages of the tree. Due to that, we use the nested distance which is able to do that job. The nested distance generalizes the Wasserstein distance to a distance of stochastic processes, or a distance of trees.

[matbesancon]

Is this documented in the docs / papers? I think this is one of the pillars of the package and should be documented as such

[kirui93]

Yes. We mentioned in the introduction that nested distance ( also called process distance or multistage distance) is used for the quality of the approximation and that it extends and generalizes the Wasserstein distance to stochastic processes.

[kirui93]

The limit on the length of the JOSS paper could not allow us to have a section for discussion of the nested distance. That is why we gave a few lines regarding it and also cited a publication discussing about this.

[matbesancon]

ok, still "Wasserstein" is used at some points as local variables, and we cannot get why from the code

[matbesancon]

Linking to the review: https://github.com/openjournals/joss-reviews/issues/1912

[kirui93]

@matbesancon It should be "Wasserstein parameter = r ". I will change that in the code.

[kirui93]

@matbesancon On the code, we changed rwasserstein to r as we are referring to the parameter r in the definition of the multistage distance. Also we managed to change the notation to transportation distance in Lattice Approximation to be consistent with our notation.