Unbalanced Optimal Transport through Non-negative Penalized Linear Regression

Contains the code relative to the paper Unbalanced Optimal Transport through Non-negative Penalized Linear Regression https://arxiv.org/abs/2106.04145

@inproceedings{chapel2021unbalanced,
  title={Unbalanced Optimal Transport through Non-negative Penalized Linear Regression},
  author={Chapel, Laetitia and Flamary, R{\'e}mi and Wu, Haoran and F{\'e}votte, C{\'e}dric and Gasso, Gilles},
  booktitle={Advances in Neural Information Processing Systems 34},
  year={2021}
}

Requirements

To install requirements:

pip install -r requirements.txt

Running

The regularization path algorithm is implemented in the Python Optimal Transport (POT) toolbox and is the latest version up-to-date.

The functions for running the algorithms can be found in the following files:

• solvers\solver_kl_UOT.py contains the functions that allows solving the KL-penalized OUT, that is
  • ot_ukl_solve_BFGS to run the BFGS algorithm
  • ot_uklreg_solve_mm to run our multiplicative algorithm
• solvers\solvers_L2_UOT.py contains the functions that allows solving the L2-penalized OUT, that is
  • ot_ul2_solve_BFGS to run the BFGS algorithm
  • ot_ul2_reg_path to compute our regularization path
  • ot_ul2_solve_lasso_celer to solve the UOT reformulated as a Lasso problem using the Celer implementation
  • ot_ul2_solve_lasso_cd to solve the UOT reformulated as a Lasso problem using the Scikit-learn implementation
  • ot_ul2_solve_mu to run our multiplicative algorithm
• solvers\solver_semirelax_L2_UOT.py contains the functions that allows solving the semi-relaxed L2-penalized OUT, that is
  • ot_semi_relaxed_ul2_reg_path to solve our regularization path algorithm

Results

Our results given in Figures 1 to 5 can be reproduced by running the following notebooks:

• Figure 1 can be reproduced by running the notebook Figure 1.ipynb

• Figure 2 can be reproduced by running the notebook Figure 2.ipynb

• Figure 3 can be reproduced by running the notebook Figure 3.ipynb

• Figure 4 can be reproduced by running the notebook Figure 4.ipynb

• Figure 5 can be reproduced by running the notebook Figure 5.ipynb