Stochastic examples — POT Python Optimal Transport 0.9.6 documentation
This example is designed to show how to use the stochastic optimization algorithms for discrete and semi-continuous measures from the POT library.
[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. Stochastic Optimization for Large-scale Optimal Transport. Advances in Neural Information Processing Systems (2016).
[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A. & Blondel, M. Large-scale Optimal Transport and Mapping Estimation. International Conference on Learning Representation (2018)
# Author: Kilian Fatras <kilian.fatras@gmail.com> # # License: MIT License import matplotlib.pylab as pl import numpy as np import ot import ot.plot
Compute the Transportation Matrix for the Semi-Dual Problem
Discrete case
Sample two discrete measures for the discrete case and compute their cost matrix c.
Call the “SAG” method to find the transportation matrix in the discrete case
[[2.55553509e-02 9.96395660e-02 1.76579142e-02 4.31178196e-06] [1.21640234e-01 1.25357448e-02 1.30225078e-03 7.37891338e-03] [3.56123975e-03 7.61451746e-02 6.31505947e-02 1.33831456e-07] [2.61515202e-02 3.34246014e-02 8.28734709e-02 4.07550428e-04] [9.85500870e-03 7.52288517e-04 1.08262628e-02 1.21423583e-01] [2.16904253e-02 9.03825797e-04 1.87178503e-03 1.18391107e-01] [4.15462212e-02 2.65987989e-02 7.23177216e-02 2.39440107e-03]]
Semi-Continuous Case
Sample one general measure a, one discrete measures b for the semicontinuous case, the points where source and target measures are defined and compute the cost matrix.
Call the “ASGD” method to find the transportation matrix in the semicontinuous case.
[3.89418541 7.69191648 3.88798203 2.63066822 1.4605918 3.30128899 2.76039982] [-2.55838411 -2.42317354 -0.84802459 5.82958224] [[2.36658434e-02 1.00210228e-01 1.89765631e-02 4.50856086e-06] [1.19762224e-01 1.34039510e-02 1.48790516e-03 8.20306258e-03] [3.18880498e-03 7.40472984e-02 6.56209042e-02 1.35308774e-07] [2.34839063e-02 3.25971567e-02 8.63628461e-02 4.13233727e-04] [8.78057873e-03 7.27931720e-04 1.11939332e-02 1.22154699e-01] [1.95469897e-02 8.84579013e-04 1.95751817e-03 1.20468056e-01] [3.77891909e-02 2.62747246e-02 7.63341399e-02 2.45908742e-03]]
Compare the results with the Sinkhorn algorithm
[[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06] [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03] [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07] [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04] [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01] [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01] [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]]
Plot Transportation Matrices
For SAG
For ASGD
For Sinkhorn
Compute the Transportation Matrix for the Dual Problem
Semi-continuous case
Sample one general measure a, one discrete measures b for the semi-continuous case and compute the cost matrix c.
Call the “SGD” dual method to find the transportation matrix in the semi-continuous case
[0.91165603 2.77176512 1.06822819 0.02120131 0.6126745 1.82423613 0.11278947] [0.33918268 0.47789947 1.5719034 4.9335652 ] [[2.17381811e-02 9.23710741e-02 1.08114235e-02 9.32409360e-08] [1.58461053e-02 1.77974690e-03 1.22107416e-04 2.44369039e-05] [3.44684454e-03 8.03203669e-02 4.39946687e-02 3.29296540e-09] [3.13249603e-02 4.36337600e-02 7.14514820e-02 1.24103327e-05] [6.81827650e-02 5.67237379e-03 5.39135941e-02 2.13564527e-02] [8.09098220e-02 3.67435169e-03 5.02563876e-03 1.12269228e-02] [4.85201684e-02 3.38544380e-02 6.07907676e-02 7.10879755e-05]]
Compare the results with the Sinkhorn algorithm
Call the Sinkhorn algorithm from POT
[[2.55553508e-02 9.96395661e-02 1.76579142e-02 4.31178193e-06] [1.21640234e-01 1.25357448e-02 1.30225079e-03 7.37891333e-03] [3.56123974e-03 7.61451746e-02 6.31505947e-02 1.33831455e-07] [2.61515201e-02 3.34246014e-02 8.28734709e-02 4.07550425e-04] [9.85500876e-03 7.52288523e-04 1.08262629e-02 1.21423583e-01] [2.16904255e-02 9.03825804e-04 1.87178504e-03 1.18391107e-01] [4.15462212e-02 2.65987989e-02 7.23177217e-02 2.39440105e-03]]
Plot Transportation Matrices
For SGD
For Sinkhorn
Total running time of the script: (0 minutes 7.197 seconds)