Optimal Transport (Spring 2020)

Project (Latest Instructions Update: March 11 2020)

The deadline for submission is Apr. 19.

Please send your

  • pdf

  • colab link with experiments/code

to marcocuturicameto+assignment@gmail.com (if you use a different email alias, your assignment may risk ending “lost” in my inbox).

Choose one topic from those presented below. If you wish to explore a different direction, send me a proposal by email.

Implement OT-GAN

In this assignment you will implement GAN variants that built on optimal transport, using a different approach than the Wasserstein-GAN paper, as proposed in the OT-Gan paper (you can also start using this variant of the same idea).

Please train your model on simple datasets (e.g. MNIST digits or simpler images). Code everything from scratch using a differentiale programming framework (TF, Jax, Autograd or PyTorch)

Sinkhorn Emebddings

Read and summarize the findings provided in a recent paper on Sinkhorn embeddings, a nice idea published very recently to visualize datapoints as point clouds. You can use this idea to embed any arbitrary family of datapoints, to define a simple MDS type criterion whose aim is to compute point cloud representations in 2D. You need to use backpropagation (e.g. using autograd, tensorflow or pytorch) to achieve this.

Does Wasserstein-GAN approximate Wasserstein distances?

The Wasserstein-GAN paper proposes a proxy for the 1-Wasserstein distance that uses neural networks. While that proxy seems to work for the task of training GANs, it is not well understood whether that approach can approximate, numerically, the Wasserstein distance. In this assignment, you will implement the W-GAN approach to solve OT and benchmark it against other approaches (e.g. Sinkhorn divergence) to study its ability to compute a quantity that is truly similar to “true” optimal transport. You should restrict yourself to low-dimensional settings (e.g. 1/2D) or to settings for which the ground truth OT distance is known (i.e. Gaussians or elliptically contoured distributions).