Optimal Transport from 1D Vector

[davibarreira]

This PR creates a version of ot_cost and ot_plan that receives usupport, vsupport and uprobs, uprobs. In case the vector of probabilities is not passed, it assumes that all entries have equal probability.

The PR has one test that is failing that I was not able to figure out where is coming from.

One thing that I tried doing was "NOT" sorting the vector, but returning the transport plan for the order given. I'm guessing this is the thing that is causing some issues, because when the transport plan is provided to the ot_cost function, it has to reorder it for to be properly used, and I'm guessing there might be some compilation issues.

[davibarreira]

The issue is type instability as I thought :(
I've written:

function ot_cost(
    c,
    usupport::AbstractVector{<:Real},
    vsupport::AbstractVector{<:Real},
    ;
    uprobs::AbstractVector{<:Real}=fill(inv(length(usupport)), length(usupport)),
    vprobs::AbstractVector{<:Real}=fill(inv(length(vsupport)), length(vsupport)),
    plan=nothing
    )
    μ = discretemeasure(usupport, uprobs)
    ν = discretemeasure(vsupport, vprobs)
    if plan === nothing
        return _ot_cost(c, μ, ν, plan)
    else
        return _ot_cost(c, μ, ν, plan[sortperm(usupport), sortperm(vsupport)])
    end
end

To try to deal with the case where the plan is the in the sorted order. But I guess this causes problems for the compiler. Any ideas on how to solve this?

[davibarreira]

Ok, so it was actually a typo in the test! This piece of code is actually solid :)

[coveralls]

Pull Request Test Coverage Report for Build 1396825672

• 11 of 11 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.2%) to 97.076%

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Totals
Change from base Build 1396587941:	0.2%
Covered Lines:	166
Relevant Lines:	171

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💛 - Coveralls

[codecov-commenter]

Codecov Report

Merging #13 (a6569be) into main (e9efd4e) will increase coverage by 0.24%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main      #13      +/-   ##
==========================================
+ Coverage   96.83%   97.07%   +0.24%     
==========================================
  Files           4        4              
  Lines         158      171      +13     
==========================================
+ Hits          153      166      +13     
  Misses          5        5              

Impacted Files	Coverage Δ
src/exact.jl	98.31% <100.00%> (+0.20%)	⬆️

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[davibarreira]

@devmotion and @zsteve , are you guys good with such kind of dispatch? This allows users to simple do:

wasserstein(rand(10),rand(10))

I'll be doing a PR for the multivariate case shortly.

[devmotion]

I am not happy about this PR. We already support OT with 1D vectors and also ot_cost, ot_plan, and wasserstein with 1D vectors. Maybe it should just be better documented.

I think we should not define ot_cost and ot_plan in this way and in particular we should not make uprobs and vprobs keyword arguments (BTW the signature in the docstring is different from the implementation). We should be consistent with the other ot_cost and ot_plan and only allow the cost and the measures (no vectors) as inputs. Users should just use discretemeasure.

In the same way, a consistent API should require them to write e.g squared2wasserstein(discretemeasure(rand(10)), discretemeasure(rand(10), probs)). This is much clearer and avoids redundant implementations.

[davibarreira]

Ok. So I guess we should export discretemeasure, since it's not currently exported. I'll make another PR here with the modification and I'll submit an update to the docs in OptimalTransport.jl. Sound good?

[coveralls]

Pull Request Test Coverage Report for Build 1396802728

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
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• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 11 of 11 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.2%) to 97.076%

---

Totals
Change from base Build 1396587941:	0.2%
Covered Lines:	166
Relevant Lines:	171

---

💛 - Coveralls