FROT

Pytorch/numpy implementation of "Feature Robust Optimal Transport for High-dimensional Data" paper:   Preprint

Installation 👷

Python requirements

This code was tested on Python 3.7 and Python 3.8, and need the following packages:

• click
• numpy
• torch
• pot
• scipy
• sklearn

You can install them with pip.

How to use 🚀

Our Frot model has a sklearn-like interface.

Toy example

Run inside a Python Interpreter:

import numpy as np
from src.models.frot import Frot

# Define some Toy data
X = np.array([[0, 0], [1, 1], [2, 2]])
Y = np.array([[0, 1], [0, 1], [2, -2]])
group = [[0], [1]]

model = Frot(eps=0.05, eta=1.0, method='sinkhorn', pFRWD=1, pnorm=2)
model.fit(X, Y, group)

PI = model.PI_
alpha = model.alpha_
dist = model.FRWD_

• PI is the optimal transport plan
• alpha is the vector which describe group importance.
• dist is the FRWD distance

Implementation

We implemented the FROT computation with 3 methods:

• lp: construct and solve a linear program
• sinkhorn: use frank-wolfe with sinkhorn as a inner solver
• emd: use frank-wolfe with emd as a inner solver

How to cite? 📋

If you find this work useful in your research, please consider citing:

@misc{petrovich2020feature,
    title={Feature Robust Optimal Transport for High-dimensional Data},
    author={Mathis Petrovich and Chao Liang and Yanbin Liu and Yao-Hung Hubert Tsai and Linchao Zhu and Yi Yang and Ruslan Salakhutdinov and Makoto Yamada},
    year={2020},
    eprint={2005.12123},
    archivePrefix={arXiv},
    primaryClass={stat.ML}
}