large-scale-OT-mapping-TF

Tensorflow Implementation of the following paper:

Title:	
Large-Scale Optimal Transport and Mapping Estimation
Authors:	
Seguy, Vivien; Bhushan Damodaran, Bharath; Flamary, Rémi; Courty, Nicolas; Rolet, Antoine; Blondel, Mathieu
Publication:	
eprint arXiv:1711.02283
Publication Date:	
11/2017
Origin:	
ARXIV
Keywords:	
Statistics - Machine Learning
Comment:	
10 pages, 4 figures
Bibliographic Code:	
2017arXiv171102283S

on arXiv

on OpenReview

Some notes

• This repository does not contain an implementation of the entire experiment of the paper. Instead, it confirms the thesis's core algorithm in a small toy example.

• Unlike the original paper, total batch-wise optimization is not implemented but I believe that it makes little difference.

• To run experiments, run run.sh.

• L2 regularization generally looks better than entropic regularization.

• Epsilon is quiet sensitive and important hyper-parameter. In my toy example, eps = 0.01 looks reasonable choice.

Requirements

python3
tensorflow
matplotlib
seaborn
...

Results (on L2 regularization)

Source and Target

Source points are green and target points are red.

Monge Map Estimation

Source points are green and transported points are blue.

KDE on transported distribution

Author

@mikigom (Junghoon Seo, Satrec Initiative)

sjh@satreci.com