OT mapping estimation for domain adaptation

This example presents how to use MappingTransport to estimate at the same time both the coupling transport and approximate the transport map with either a linear or a kernelized mapping as introduced in [8].

[8] M. Perrot, N. Courty, R. Flamary, A. Habrard, “Mapping estimation for discrete optimal transport”, Neural Information Processing Systems (NIPS), 2016.

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

# sphinx_gallery_thumbnail_number = 2

import numpy as np
import matplotlib.pylab as pl
import ot

Generate data

n_source_samples = 100
n_target_samples = 100
theta = 2 * np.pi / 20
noise_level = 0.1

Xs, ys = ot.datasets.make_data_classif(
    'gaussrot', n_source_samples, nz=noise_level)
Xs_new, _ = ot.datasets.make_data_classif(
    'gaussrot', n_source_samples, nz=noise_level)
Xt, yt = ot.datasets.make_data_classif(
    'gaussrot', n_target_samples, theta=theta, nz=noise_level)

# one of the target mode changes its variance (no linear mapping)
Xt[yt == 2] *= 3
Xt = Xt + 4

Plot data

pl.figure(1, (10, 5))
pl.clf()
pl.scatter(Xs[:, 0], Xs[:, 1], c=ys, marker='+', label='Source samples')
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o', label='Target samples')
pl.legend(loc=0)
pl.title('Source and target distributions')

Out:

Text(0.5, 1.0, 'Source and target distributions')

Instantiate the different transport algorithms and fit them

# MappingTransport with linear kernel
ot_mapping_linear = ot.da.MappingTransport(
    kernel="linear", mu=1e0, eta=1e-8, bias=True,
    max_iter=20, verbose=True)

ot_mapping_linear.fit(Xs=Xs, Xt=Xt)

# for original source samples, transform applies barycentric mapping
transp_Xs_linear = ot_mapping_linear.transform(Xs=Xs)

# for out of source samples, transform applies the linear mapping
transp_Xs_linear_new = ot_mapping_linear.transform(Xs=Xs_new)


# MappingTransport with gaussian kernel
ot_mapping_gaussian = ot.da.MappingTransport(
    kernel="gaussian", eta=1e-5, mu=1e-1, bias=True, sigma=1,
    max_iter=10, verbose=True)
ot_mapping_gaussian.fit(Xs=Xs, Xt=Xt)

# for original source samples, transform applies barycentric mapping
transp_Xs_gaussian = ot_mapping_gaussian.transform(Xs=Xs)

# for out of source samples, transform applies the gaussian mapping
transp_Xs_gaussian_new = ot_mapping_gaussian.transform(Xs=Xs_new)

Out:

It.  |Loss        |Delta loss
--------------------------------
    0|4.328362e+03|0.000000e+00
    1|4.310439e+03|-4.140948e-03
    2|4.309902e+03|-1.244927e-04
    3|4.309730e+03|-4.006511e-05
    4|4.309645e+03|-1.957040e-05
    5|4.309590e+03|-1.290080e-05
    6|4.309585e+03|-9.743232e-07
It.  |Loss        |Delta loss
--------------------------------
    0|4.337332e+02|0.000000e+00
    1|4.290396e+02|-1.082153e-02
    2|4.287689e+02|-6.307954e-04
    3|4.286256e+02|-3.342203e-04
    4|4.285333e+02|-2.154645e-04
    5|4.284674e+02|-1.537909e-04
    6|4.284192e+02|-1.124518e-04
    7|4.283817e+02|-8.742801e-05
    8|4.283535e+02|-6.593065e-05
    9|4.283306e+02|-5.347355e-05
   10|4.283104e+02|-4.705427e-05

Plot transported samples

pl.figure(2)
pl.clf()
pl.subplot(2, 2, 1)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
           label='Target samples', alpha=.2)
pl.scatter(transp_Xs_linear[:, 0], transp_Xs_linear[:, 1], c=ys, marker='+',
           label='Mapped source samples')
pl.title("Bary. mapping (linear)")
pl.legend(loc=0)

pl.subplot(2, 2, 2)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
           label='Target samples', alpha=.2)
pl.scatter(transp_Xs_linear_new[:, 0], transp_Xs_linear_new[:, 1],
           c=ys, marker='+', label='Learned mapping')
pl.title("Estim. mapping (linear)")

pl.subplot(2, 2, 3)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
           label='Target samples', alpha=.2)
pl.scatter(transp_Xs_gaussian[:, 0], transp_Xs_gaussian[:, 1], c=ys,
           marker='+', label='barycentric mapping')
pl.title("Bary. mapping (kernel)")

pl.subplot(2, 2, 4)
pl.scatter(Xt[:, 0], Xt[:, 1], c=yt, marker='o',
           label='Target samples', alpha=.2)
pl.scatter(transp_Xs_gaussian_new[:, 0], transp_Xs_gaussian_new[:, 1], c=ys,
           marker='+', label='Learned mapping')
pl.title("Estim. mapping (kernel)")
pl.tight_layout()

pl.show()