OT for domain adaptation

Note

Example added in release: 0.1.9.

This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently supported in POT.

# Authors: Remi Flamary <remi.flamary@unice.fr>
#          Stanislas Chambon <stan.chambon@gmail.com>
#
# License: MIT License

import matplotlib.pylab as pl
import ot

Generate data

n_source_samples = 150
n_target_samples = 150

Xs, ys = ot.datasets.make_data_classif("3gauss", n_source_samples)
Xt, yt = ot.datasets.make_data_classif("3gauss2", n_target_samples)

Instantiate the different transport algorithms and fit them

# EMD Transport
ot_emd = ot.da.EMDTransport()
ot_emd.fit(Xs=Xs, Xt=Xt)

# Sinkhorn Transport
ot_sinkhorn = ot.da.SinkhornTransport(reg_e=1e-1)
ot_sinkhorn.fit(Xs=Xs, Xt=Xt)

# Sinkhorn Transport with Group lasso regularization
ot_lpl1 = ot.da.SinkhornLpl1Transport(reg_e=1e-1, reg_cl=1e0)
ot_lpl1.fit(Xs=Xs, ys=ys, Xt=Xt)

# Sinkhorn Transport with Group lasso regularization l1l2
ot_l1l2 = ot.da.SinkhornL1l2Transport(reg_e=1e-1, reg_cl=2e0, max_iter=20, verbose=True)
ot_l1l2.fit(Xs=Xs, ys=ys, Xt=Xt)

# transport source samples onto target samples
transp_Xs_emd = ot_emd.transform(Xs=Xs)
transp_Xs_sinkhorn = ot_sinkhorn.transform(Xs=Xs)
transp_Xs_lpl1 = ot_lpl1.transform(Xs=Xs)
transp_Xs_l1l2 = ot_l1l2.transform(Xs=Xs)

/home/circleci/project/ot/bregman/_sinkhorn.py:902: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
  warnings.warn(
/home/circleci/project/ot/bregman/_sinkhorn.py:666: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
  warnings.warn(
It.  |Loss        |Relative loss|Absolute loss
------------------------------------------------
    0|1.076519e+01|0.000000e+00|0.000000e+00
    1|2.789939e+00|2.858574e+00|7.975249e+00
    2|2.604436e+00|7.122582e-02|1.855031e-01
    3|2.564931e+00|1.540200e-02|3.950507e-02
    4|2.552730e+00|4.779631e-03|1.220111e-02
    5|2.549066e+00|1.437414e-03|3.664062e-03
    6|2.546184e+00|1.131874e-03|2.881959e-03
    7|2.541609e+00|1.800045e-03|4.575011e-03
    8|2.536793e+00|1.898383e-03|4.815806e-03
    9|2.532860e+00|1.553007e-03|3.933550e-03
   10|2.530491e+00|9.361469e-04|2.368911e-03
   11|2.529203e+00|5.091913e-04|1.287848e-03
   12|2.528502e+00|2.773673e-04|7.013238e-04
   13|2.528137e+00|1.441848e-04|3.645189e-04
   14|2.528036e+00|3.998149e-05|1.010746e-04
   15|2.527504e+00|2.106363e-04|5.323840e-04
   16|2.526725e+00|3.079986e-04|7.782278e-04
   17|2.526554e+00|6.789926e-05|1.715511e-04
   18|2.526356e+00|7.819090e-05|1.975381e-04
   19|2.525902e+00|1.799791e-04|4.546095e-04
It.  |Loss        |Relative loss|Absolute loss
------------------------------------------------
   20|2.525797e+00|4.153716e-05|1.049144e-04

Fig 1 : plots source and target samples

pl.figure(1, figsize=(10, 5))
pl.subplot(1, 2, 1)
pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker="+", label="Source samples")
pl.xticks([])
pl.yticks([])
pl.legend(loc=0)
pl.title("Source  samples")

pl.subplot(1, 2, 2)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples")
pl.xticks([])
pl.yticks([])
pl.legend(loc=0)
pl.title("Target samples")
pl.tight_layout()

Fig 2 : plot optimal couplings and transported samples

param_img = {"interpolation": "nearest", "cmap": "gray_r"}

pl.figure(2, figsize=(15, 8))
pl.subplot(2, 4, 1)
pl.imshow(ot_emd.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nEMDTransport")

pl.subplot(2, 4, 2)
pl.imshow(ot_sinkhorn.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nSinkhornTransport")

pl.subplot(2, 4, 3)
pl.imshow(ot_lpl1.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nSinkhornLpl1Transport")

pl.subplot(2, 4, 4)
pl.imshow(ot_l1l2.coupling_, **param_img)
pl.xticks([])
pl.yticks([])
pl.title("Optimal coupling\nSinkhornL1l2Transport")

pl.subplot(2, 4, 5)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_emd[:, 0],
    transp_Xs_emd[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nEmdTransport")
pl.legend(loc="lower left")

pl.subplot(2, 4, 6)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_sinkhorn[:, 0],
    transp_Xs_sinkhorn[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nSinkhornTransport")

pl.subplot(2, 4, 7)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_lpl1[:, 0],
    transp_Xs_lpl1[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nSinkhornLpl1Transport")

pl.subplot(2, 4, 8)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker="o", label="Target samples", alpha=0.3)
pl.scatter(
    transp_Xs_l1l2[:, 0],
    transp_Xs_l1l2[:, 1],
    c=ys,
    marker="+",
    label="Transp samples",
    s=30,
)
pl.xticks([])
pl.yticks([])
pl.title("Transported samples\nSinkhornL1l2Transport")
pl.tight_layout()

pl.show()