added optimal transport example

[sbarratt]

@olivierteboul can you take a look at this?

[sbarratt]

@akshayka

[bamos]

I think this is the same as Eq (3) of https://arxiv.org/abs/1802.08665, right?

If so, it would be cool to mention the connection to that paper, and to https://arxiv.org/abs/1106.1925, since they differentiate through that convex optimization problem by unrolling the sinkhorn iterates. (Which is exact if the sinkhorn iterates converge)

[sbarratt]

Yeah, that's exactly it. I based it off of https://papers.nips.cc/paper/8910-differentiable-ranking-and-sorting-using-optimal-transport.pdf .

I'll add some references so we can connect it to prior work.

On Tue, Apr 14, 2020 at 11:47 AM Brandon Amos [email protected] wrote:

I think this is the same as Eq (3) of https://arxiv.org/abs/1802.08665, right?

[image: image] https://user-images.githubusercontent.com/707462/79261798-5bc6c400-7e5e-11ea-86f1-171bc72be207.png

If so, it would be cool to mention the connection to that paper, and to https://arxiv.org/abs/1106.1925, since they differentiate through that convex optimization problem by unrolling the sinkhorn iterates. (Which is exact if the sinkhorn iterates converge)

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[akshayka]

Sorry for the late response ...!

Looks mostly good! Just a few comments.

1. I was confused by the wording in the first sentence, since the support of a probability distribution is typically a set, not a vector.
2. The LaTeX isn't rendering correctly. I'm looking here: https://github.com/cvxgrp/cvxpylayers/blob/970163a34770bca0daac7cb727627e45fa03c169/examples/torch/optimal_transport.ipynb
3. Maybe include axis labels on the plot, to explain what's being visualized?

[akshayka]

LGTM modulo the comments I made previously.