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test_gromov.py
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"""Tests for module gromov """
# Author: Erwan Vautier <[email protected]>
# Nicolas Courty <[email protected]>
# Titouan Vayer <[email protected]>
# Cédric Vincent-Cuaz <[email protected]>
#
# License: MIT License
import numpy as np
import ot
from ot.backend import NumpyBackend
from ot.backend import torch, tf
import pytest
def test_gromov(nx):
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=4)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
G0 = p[:, None] * q[None, :]
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
G0b = nx.from_numpy(G0)
G = ot.gromov.gromov_wasserstein(C1, C2, p, q, 'square_loss', G0=G0, verbose=True)
Gb = nx.to_numpy(ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', G0=G0b, verbose=True))
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
Id = (1 / (1.0 * n_samples)) * np.eye(n_samples, n_samples)
np.testing.assert_allclose(Gb, np.flipud(Id), atol=1e-04)
gw, log = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', log=True)
gwb, logb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', log=True)
gwb = nx.to_numpy(gwb)
gw_val = ot.gromov.gromov_wasserstein2(C1, C2, p, q, 'kl_loss', G0=G0, log=False)
gw_valb = nx.to_numpy(
ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', G0=G0b, log=False)
)
G = log['T']
Gb = nx.to_numpy(logb['T'])
np.testing.assert_allclose(gw, gwb, atol=1e-06)
np.testing.assert_allclose(gwb, 0, atol=1e-1, rtol=1e-1)
np.testing.assert_allclose(gw_val, gw_valb, atol=1e-06)
np.testing.assert_allclose(gwb, gw_valb, atol=1e-1, rtol=1e-1) # cf log=False
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
def test_gromov_dtype_device(nx):
# setup
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=4)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
G0 = p[:, None] * q[None, :]
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
C1b = nx.from_numpy(C1, type_as=tp)
C2b = nx.from_numpy(C2, type_as=tp)
pb = nx.from_numpy(p, type_as=tp)
qb = nx.from_numpy(q, type_as=tp)
G0b = nx.from_numpy(G0, type_as=tp)
Gb = ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', G0=G0b, verbose=True)
gw_valb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', G0=G0b, log=False)
nx.assert_same_dtype_device(C1b, Gb)
nx.assert_same_dtype_device(C1b, gw_valb)
@pytest.mark.skipif(not tf, reason="tf not installed")
def test_gromov_device_tf():
nx = ot.backend.TensorflowBackend()
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=4)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
G0 = p[:, None] * q[None, :]
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
# Check that everything stays on the CPU
with tf.device("/CPU:0"):
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
G0b = nx.from_numpy(G0)
Gb = ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', G0=G0b, verbose=True)
gw_valb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', G0=G0b, log=False)
nx.assert_same_dtype_device(C1b, Gb)
nx.assert_same_dtype_device(C1b, gw_valb)
if len(tf.config.list_physical_devices('GPU')) > 0:
# Check that everything happens on the GPU
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
G0b = nx.from_numpy(G0b)
Gb = ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', verbose=True)
gw_valb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', log=False)
nx.assert_same_dtype_device(C1b, Gb)
nx.assert_same_dtype_device(C1b, gw_valb)
assert nx.dtype_device(Gb)[1].startswith("GPU")
def test_gromov2_gradients():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=4)
xt = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=5)
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
if torch:
p1 = torch.tensor(p, requires_grad=True)
q1 = torch.tensor(q, requires_grad=True)
C11 = torch.tensor(C1, requires_grad=True)
C12 = torch.tensor(C2, requires_grad=True)
val = ot.gromov_wasserstein2(C11, C12, p1, q1)
val.backward()
assert q1.shape == q1.grad.shape
assert p1.shape == p1.grad.shape
assert C11.shape == C11.grad.shape
assert C12.shape == C12.grad.shape
@pytest.skip_backend("jax", reason="test very slow with jax backend")
@pytest.skip_backend("tf", reason="test very slow with tf backend")
def test_entropic_gromov(nx):
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
G = ot.gromov.entropic_gromov_wasserstein(
C1, C2, p, q, 'square_loss', epsilon=5e-4, verbose=True)
Gb = nx.to_numpy(ot.gromov.entropic_gromov_wasserstein(
C1b, C2b, pb, qb, 'square_loss', epsilon=5e-4, verbose=True
))
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
gw, log = ot.gromov.entropic_gromov_wasserstein2(
C1, C2, p, q, 'kl_loss', epsilon=1e-2, log=True)
gwb, logb = ot.gromov.entropic_gromov_wasserstein2(
C1b, C2b, pb, qb, 'kl_loss', epsilon=1e-2, log=True)
gwb = nx.to_numpy(gwb)
G = log['T']
Gb = nx.to_numpy(logb['T'])
np.testing.assert_allclose(gw, gwb, atol=1e-06)
np.testing.assert_allclose(gw, 0, atol=1e-1, rtol=1e-1)
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
@pytest.skip_backend("jax", reason="test very slow with jax backend")
@pytest.skip_backend("tf", reason="test very slow with tf backend")
def test_entropic_gromov_dtype_device(nx):
# setup
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
for tp in nx.__type_list__:
print(nx.dtype_device(tp))
C1b = nx.from_numpy(C1, type_as=tp)
C2b = nx.from_numpy(C2, type_as=tp)
pb = nx.from_numpy(p, type_as=tp)
qb = nx.from_numpy(q, type_as=tp)
Gb = ot.gromov.entropic_gromov_wasserstein(
C1b, C2b, pb, qb, 'square_loss', epsilon=5e-4, verbose=True
)
gw_valb = ot.gromov.entropic_gromov_wasserstein2(
C1b, C2b, pb, qb, 'square_loss', epsilon=5e-4, verbose=True
)
nx.assert_same_dtype_device(C1b, Gb)
nx.assert_same_dtype_device(C1b, gw_valb)
def test_pointwise_gromov(nx):
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
def loss(x, y):
return np.abs(x - y)
def lossb(x, y):
return nx.abs(x - y)
G, log = ot.gromov.pointwise_gromov_wasserstein(
C1, C2, p, q, loss, max_iter=100, log=True, verbose=True, random_state=42)
G = NumpyBackend().todense(G)
Gb, logb = ot.gromov.pointwise_gromov_wasserstein(
C1b, C2b, pb, qb, lossb, max_iter=100, log=True, verbose=True, random_state=42)
Gb = nx.to_numpy(nx.todense(Gb))
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(float(logb['gw_dist_estimated']), 0.0, atol=1e-08)
np.testing.assert_allclose(float(logb['gw_dist_std']), 0.0, atol=1e-08)
G, log = ot.gromov.pointwise_gromov_wasserstein(
C1, C2, p, q, loss, max_iter=100, alpha=0.1, log=True, verbose=True, random_state=42)
G = NumpyBackend().todense(G)
Gb, logb = ot.gromov.pointwise_gromov_wasserstein(
C1b, C2b, pb, qb, lossb, max_iter=100, alpha=0.1, log=True, verbose=True, random_state=42)
Gb = nx.to_numpy(nx.todense(Gb))
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(float(logb['gw_dist_estimated']), 0.10342276348494964, atol=1e-8)
np.testing.assert_allclose(float(logb['gw_dist_std']), 0.0015952535464736394, atol=1e-8)
@pytest.skip_backend("tf", reason="test very slow with tf backend")
@pytest.skip_backend("jax", reason="test very slow with jax backend")
def test_sampled_gromov(nx):
n_samples = 50 # nb samples
mu_s = np.array([0, 0], dtype=np.float64)
cov_s = np.array([[1, 0], [0, 1]], dtype=np.float64)
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
def loss(x, y):
return np.abs(x - y)
def lossb(x, y):
return nx.abs(x - y)
G, log = ot.gromov.sampled_gromov_wasserstein(
C1, C2, p, q, loss, max_iter=100, epsilon=1, log=True, verbose=True, random_state=42)
Gb, logb = ot.gromov.sampled_gromov_wasserstein(
C1b, C2b, pb, qb, lossb, max_iter=100, epsilon=1, log=True, verbose=True, random_state=42)
Gb = nx.to_numpy(Gb)
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(float(logb['gw_dist_estimated']), 0.05679474884977278, atol=1e-08)
np.testing.assert_allclose(float(logb['gw_dist_std']), 0.0005986592106971995, atol=1e-08)
def test_gromov_barycenter(nx):
ns = 10
nt = 20
Xs, ys = ot.datasets.make_data_classif('3gauss', ns, random_state=42)
Xt, yt = ot.datasets.make_data_classif('3gauss2', nt, random_state=42)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
p1 = ot.unif(ns)
p2 = ot.unif(nt)
n_samples = 3
p = ot.unif(n_samples)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
p1b = nx.from_numpy(p1)
p2b = nx.from_numpy(p2)
pb = nx.from_numpy(p)
Cb = ot.gromov.gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'square_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42
)
Cbb = nx.to_numpy(ot.gromov.gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'square_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42
))
np.testing.assert_allclose(Cb, Cbb, atol=1e-06)
np.testing.assert_allclose(Cbb.shape, (n_samples, n_samples))
# test of gromov_barycenters with `log` on
Cb_, err_ = ot.gromov.gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'square_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cbb_, errb_ = ot.gromov.gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'square_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cbb_ = nx.to_numpy(Cbb_)
np.testing.assert_allclose(Cb_, Cbb_, atol=1e-06)
np.testing.assert_array_almost_equal(err_['err'], errb_['err'])
np.testing.assert_allclose(Cbb_.shape, (n_samples, n_samples))
Cb2 = ot.gromov.gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'kl_loss', max_iter=100, tol=1e-3, random_state=42
)
Cb2b = nx.to_numpy(ot.gromov.gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'kl_loss', max_iter=100, tol=1e-3, random_state=42
))
np.testing.assert_allclose(Cb2, Cb2b, atol=1e-06)
np.testing.assert_allclose(Cb2b.shape, (n_samples, n_samples))
# test of gromov_barycenters with `log` on
Cb2_, err2_ = ot.gromov.gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'kl_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cb2b_, err2b_ = ot.gromov.gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'kl_loss', max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cb2b_ = nx.to_numpy(Cb2b_)
np.testing.assert_allclose(Cb2_, Cb2b_, atol=1e-06)
np.testing.assert_array_almost_equal(err2_['err'], err2_['err'])
np.testing.assert_allclose(Cb2b_.shape, (n_samples, n_samples))
@pytest.mark.filterwarnings("ignore:divide")
def test_gromov_entropic_barycenter(nx):
ns = 10
nt = 20
Xs, ys = ot.datasets.make_data_classif('3gauss', ns, random_state=42)
Xt, yt = ot.datasets.make_data_classif('3gauss2', nt, random_state=42)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
p1 = ot.unif(ns)
p2 = ot.unif(nt)
n_samples = 2
p = ot.unif(n_samples)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
p1b = nx.from_numpy(p1)
p2b = nx.from_numpy(p2)
pb = nx.from_numpy(p)
Cb = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'square_loss', 1e-3, max_iter=50, tol=1e-3, verbose=True, random_state=42
)
Cbb = nx.to_numpy(ot.gromov.entropic_gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'square_loss', 1e-3, max_iter=50, tol=1e-3, verbose=True, random_state=42
))
np.testing.assert_allclose(Cb, Cbb, atol=1e-06)
np.testing.assert_allclose(Cbb.shape, (n_samples, n_samples))
# test of entropic_gromov_barycenters with `log` on
Cb_, err_ = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'square_loss', 1e-3, max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cbb_, errb_ = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'square_loss', 1e-3, max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cbb_ = nx.to_numpy(Cbb_)
np.testing.assert_allclose(Cb_, Cbb_, atol=1e-06)
np.testing.assert_array_almost_equal(err_['err'], errb_['err'])
np.testing.assert_allclose(Cbb_.shape, (n_samples, n_samples))
Cb2 = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'kl_loss', 1e-3, max_iter=100, tol=1e-3, random_state=42
)
Cb2b = nx.to_numpy(ot.gromov.entropic_gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'kl_loss', 1e-3, max_iter=100, tol=1e-3, random_state=42
))
np.testing.assert_allclose(Cb2, Cb2b, atol=1e-06)
np.testing.assert_allclose(Cb2b.shape, (n_samples, n_samples))
# test of entropic_gromov_barycenters with `log` on
Cb2_, err2_ = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1, C2], [p1, p2], p, [.5, .5],
'kl_loss', 1e-3, max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cb2b_, err2b_ = ot.gromov.entropic_gromov_barycenters(
n_samples, [C1b, C2b], [p1b, p2b], pb, [.5, .5],
'kl_loss', 1e-3, max_iter=100, tol=1e-3, verbose=True, random_state=42, log=True
)
Cb2b_ = nx.to_numpy(Cb2b_)
np.testing.assert_allclose(Cb2_, Cb2b_, atol=1e-06)
np.testing.assert_array_almost_equal(err2_['err'], err2_['err'])
np.testing.assert_allclose(Cb2b_.shape, (n_samples, n_samples))
def test_fgw(nx):
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=42)
xt = xs[::-1].copy()
ys = np.random.randn(xs.shape[0], 2)
yt = ys[::-1].copy()
p = ot.unif(n_samples)
q = ot.unif(n_samples)
G0 = p[:, None] * q[None, :]
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
M = ot.dist(ys, yt)
M /= M.max()
Mb = nx.from_numpy(M)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
pb = nx.from_numpy(p)
qb = nx.from_numpy(q)
G0b = nx.from_numpy(G0)
G, log = ot.gromov.fused_gromov_wasserstein(M, C1, C2, p, q, 'square_loss', alpha=0.5, G0=G0, log=True)
Gb, logb = ot.gromov.fused_gromov_wasserstein(Mb, C1b, C2b, pb, qb, 'square_loss', alpha=0.5, G0=G0b, log=True)
Gb = nx.to_numpy(Gb)
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence fgw
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence fgw
Id = (1 / (1.0 * n_samples)) * np.eye(n_samples, n_samples)
np.testing.assert_allclose(
Gb, np.flipud(Id), atol=1e-04) # cf convergence gromov
fgw, log = ot.gromov.fused_gromov_wasserstein2(M, C1, C2, p, q, 'square_loss', G0=None, alpha=0.5, log=True)
fgwb, logb = ot.gromov.fused_gromov_wasserstein2(Mb, C1b, C2b, pb, qb, 'square_loss', G0=G0b, alpha=0.5, log=True)
fgwb = nx.to_numpy(fgwb)
G = log['T']
Gb = nx.to_numpy(logb['T'])
np.testing.assert_allclose(fgw, fgwb, atol=1e-08)
np.testing.assert_allclose(fgwb, 0, atol=1e-1, rtol=1e-1)
# check constraints
np.testing.assert_allclose(G, Gb, atol=1e-06)
np.testing.assert_allclose(
p, Gb.sum(1), atol=1e-04) # cf convergence gromov
np.testing.assert_allclose(
q, Gb.sum(0), atol=1e-04) # cf convergence gromov
def test_fgw2_gradients():
n_samples = 50 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=4)
xt = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s, random_state=5)
p = ot.unif(n_samples)
q = ot.unif(n_samples)
C1 = ot.dist(xs, xs)
C2 = ot.dist(xt, xt)
M = ot.dist(xs, xt)
C1 /= C1.max()
C2 /= C2.max()
if torch:
p1 = torch.tensor(p, requires_grad=True)
q1 = torch.tensor(q, requires_grad=True)
C11 = torch.tensor(C1, requires_grad=True)
C12 = torch.tensor(C2, requires_grad=True)
M1 = torch.tensor(M, requires_grad=True)
val = ot.fused_gromov_wasserstein2(M1, C11, C12, p1, q1)
val.backward()
assert q1.shape == q1.grad.shape
assert p1.shape == p1.grad.shape
assert C11.shape == C11.grad.shape
assert C12.shape == C12.grad.shape
assert M1.shape == M1.grad.shape
def test_fgw_barycenter(nx):
np.random.seed(42)
ns = 50
nt = 60
Xs, ys = ot.datasets.make_data_classif('3gauss', ns, random_state=42)
Xt, yt = ot.datasets.make_data_classif('3gauss2', nt, random_state=42)
ys = np.random.randn(Xs.shape[0], 2)
yt = np.random.randn(Xt.shape[0], 2)
C1 = ot.dist(Xs)
C2 = ot.dist(Xt)
p1, p2 = ot.unif(ns), ot.unif(nt)
n_samples = 3
p = ot.unif(n_samples)
ysb = nx.from_numpy(ys)
ytb = nx.from_numpy(yt)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
p1b = nx.from_numpy(p1)
p2b = nx.from_numpy(p2)
pb = nx.from_numpy(p)
Xb, Cb = ot.gromov.fgw_barycenters(
n_samples, [ysb, ytb], [C1b, C2b], [p1b, p2b], [.5, .5], 0.5, fixed_structure=False,
fixed_features=False, p=pb, loss_fun='square_loss', max_iter=100, tol=1e-3, random_state=12345
)
xalea = np.random.randn(n_samples, 2)
init_C = ot.dist(xalea, xalea)
init_Cb = nx.from_numpy(init_C)
Xb, Cb = ot.gromov.fgw_barycenters(
n_samples, [ysb, ytb], [C1b, C2b], ps=[p1b, p2b], lambdas=[.5, .5],
alpha=0.5, fixed_structure=True, init_C=init_Cb, fixed_features=False,
p=pb, loss_fun='square_loss', max_iter=100, tol=1e-3
)
Xb, Cb = nx.to_numpy(Xb), nx.to_numpy(Cb)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
np.testing.assert_allclose(Xb.shape, (n_samples, ys.shape[1]))
init_X = np.random.randn(n_samples, ys.shape[1])
init_Xb = nx.from_numpy(init_X)
Xb, Cb, logb = ot.gromov.fgw_barycenters(
n_samples, [ysb, ytb], [C1b, C2b], [p1b, p2b], [.5, .5], 0.5,
fixed_structure=False, fixed_features=True, init_X=init_Xb,
p=pb, loss_fun='square_loss', max_iter=100, tol=1e-3, log=True, random_state=98765
)
Xb, Cb = nx.to_numpy(Xb), nx.to_numpy(Cb)
np.testing.assert_allclose(Cb.shape, (n_samples, n_samples))
np.testing.assert_allclose(Xb.shape, (n_samples, ys.shape[1]))
def test_gromov_wasserstein_linear_unmixing(nx):
n = 10
X1, y1 = ot.datasets.make_data_classif('3gauss', n, random_state=42)
X2, y2 = ot.datasets.make_data_classif('3gauss2', n, random_state=42)
C1 = ot.dist(X1)
C2 = ot.dist(X2)
Cdict = np.stack([C1, C2])
p = ot.unif(n)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
Cdictb = nx.from_numpy(Cdict)
pb = nx.from_numpy(p)
tol = 10**(-5)
# Tests without regularization
reg = 0.
unmixing1, C1_emb, OT, reconstruction1 = ot.gromov.gromov_wasserstein_linear_unmixing(
C1, Cdict, reg=reg, p=p, q=p,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing1b, C1b_emb, OTb, reconstruction1b = ot.gromov.gromov_wasserstein_linear_unmixing(
C1b, Cdictb, reg=reg, p=None, q=None,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing2, C2_emb, OT, reconstruction2 = ot.gromov.gromov_wasserstein_linear_unmixing(
C2, Cdict, reg=reg, p=None, q=None,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing2b, C2b_emb, OTb, reconstruction2b = ot.gromov.gromov_wasserstein_linear_unmixing(
C2b, Cdictb, reg=reg, p=pb, q=pb,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
np.testing.assert_allclose(unmixing1, nx.to_numpy(unmixing1b), atol=1e-06)
np.testing.assert_allclose(unmixing1, [1., 0.], atol=1e-01)
np.testing.assert_allclose(unmixing2, nx.to_numpy(unmixing2b), atol=1e-06)
np.testing.assert_allclose(unmixing2, [0., 1.], atol=1e-01)
np.testing.assert_allclose(C1_emb, nx.to_numpy(C1b_emb), atol=1e-06)
np.testing.assert_allclose(C2_emb, nx.to_numpy(C2b_emb), atol=1e-06)
np.testing.assert_allclose(reconstruction1, reconstruction1b, atol=1e-06)
np.testing.assert_allclose(reconstruction2, reconstruction2b, atol=1e-06)
np.testing.assert_allclose(C1b_emb.shape, (n, n))
np.testing.assert_allclose(C2b_emb.shape, (n, n))
# Tests with regularization
reg = 0.001
unmixing1, C1_emb, OT, reconstruction1 = ot.gromov.gromov_wasserstein_linear_unmixing(
C1, Cdict, reg=reg, p=p, q=p,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing1b, C1b_emb, OTb, reconstruction1b = ot.gromov.gromov_wasserstein_linear_unmixing(
C1b, Cdictb, reg=reg, p=None, q=None,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing2, C2_emb, OT, reconstruction2 = ot.gromov.gromov_wasserstein_linear_unmixing(
C2, Cdict, reg=reg, p=None, q=None,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
unmixing2b, C2b_emb, OTb, reconstruction2b = ot.gromov.gromov_wasserstein_linear_unmixing(
C2b, Cdictb, reg=reg, p=pb, q=pb,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
np.testing.assert_allclose(unmixing1, nx.to_numpy(unmixing1b), atol=1e-06)
np.testing.assert_allclose(unmixing1, [1., 0.], atol=1e-01)
np.testing.assert_allclose(unmixing2, nx.to_numpy(unmixing2b), atol=1e-06)
np.testing.assert_allclose(unmixing2, [0., 1.], atol=1e-01)
np.testing.assert_allclose(C1_emb, nx.to_numpy(C1b_emb), atol=1e-06)
np.testing.assert_allclose(C2_emb, nx.to_numpy(C2b_emb), atol=1e-06)
np.testing.assert_allclose(reconstruction1, reconstruction1b, atol=1e-06)
np.testing.assert_allclose(reconstruction2, reconstruction2b, atol=1e-06)
np.testing.assert_allclose(C1b_emb.shape, (n, n))
np.testing.assert_allclose(C2b_emb.shape, (n, n))
def test_gromov_wasserstein_dictionary_learning(nx):
# create dataset composed from 2 structures which are repeated 5 times
shape = 10
n_samples = 2
n_atoms = 2
projection = 'nonnegative_symmetric'
X1, y1 = ot.datasets.make_data_classif('3gauss', shape, random_state=42)
X2, y2 = ot.datasets.make_data_classif('3gauss2', shape, random_state=42)
C1 = ot.dist(X1)
C2 = ot.dist(X2)
Cs = [C1.copy() for _ in range(n_samples // 2)] + [C2.copy() for _ in range(n_samples // 2)]
ps = [ot.unif(shape) for _ in range(n_samples)]
q = ot.unif(shape)
# Provide initialization for the graph dictionary of shape (n_atoms, shape, shape)
# following the same procedure than implemented in gromov_wasserstein_dictionary_learning.
dataset_means = [C.mean() for C in Cs]
np.random.seed(0)
Cdict_init = np.random.normal(loc=np.mean(dataset_means), scale=np.std(dataset_means), size=(n_atoms, shape, shape))
if projection == 'nonnegative_symmetric':
Cdict_init = 0.5 * (Cdict_init + Cdict_init.transpose((0, 2, 1)))
Cdict_init[Cdict_init < 0.] = 0.
Csb = [nx.from_numpy(C) for C in Cs]
psb = [nx.from_numpy(p) for p in ps]
qb = nx.from_numpy(q)
Cdict_initb = nx.from_numpy(Cdict_init)
# Test: compare reconstruction error using initial dictionary and dictionary learned using this initialization
# > Compute initial reconstruction of samples on this random dictionary without backend
use_adam_optimizer = True
verbose = False
tol = 10**(-5)
epochs = 1
initial_total_reconstruction = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Cs[i], Cdict_init, p=ps[i], q=q, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
initial_total_reconstruction += reconstruction
# > Learn the dictionary using this init
Cdict, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Cs, D=n_atoms, nt=shape, ps=ps, q=q, Cdict_init=Cdict_init,
epochs=epochs, batch_size=2 * n_samples, learning_rate=1., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=False, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# > Compute reconstruction of samples on learned dictionary without backend
total_reconstruction = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Cs[i], Cdict, p=None, q=None, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction += reconstruction
np.testing.assert_array_less(total_reconstruction, initial_total_reconstruction)
# Test: Perform same experiments after going through backend
Cdictb, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Csb, D=n_atoms, nt=shape, ps=None, q=None, Cdict_init=Cdict_initb,
epochs=epochs, batch_size=n_samples, learning_rate=1., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=False, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# Compute reconstruction of samples on learned dictionary
total_reconstruction_b = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Csb[i], Cdictb, p=psb[i], q=qb, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction_b += reconstruction
np.testing.assert_array_less(total_reconstruction_b, initial_total_reconstruction)
np.testing.assert_allclose(total_reconstruction_b, total_reconstruction, atol=1e-05)
np.testing.assert_allclose(total_reconstruction_b, total_reconstruction, atol=1e-05)
np.testing.assert_allclose(Cdict, nx.to_numpy(Cdictb), atol=1e-03)
# Test: Perform same comparison without providing the initial dictionary being an optional input
# knowing than the initialization scheme is the same than implemented to set the benchmarked initialization.
np.random.seed(0)
Cdict_bis, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Cs, D=n_atoms, nt=shape, ps=None, q=None, Cdict_init=None,
epochs=epochs, batch_size=n_samples, learning_rate=1., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=False, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# > Compute reconstruction of samples on learned dictionary
total_reconstruction_bis = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Cs[i], Cdict_bis, p=ps[i], q=q, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction_bis += reconstruction
np.testing.assert_allclose(total_reconstruction_bis, total_reconstruction, atol=1e-05)
# Test: Same after going through backend
np.random.seed(0)
Cdictb_bis, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Csb, D=n_atoms, nt=shape, ps=psb, q=qb, Cdict_init=None,
epochs=epochs, batch_size=n_samples, learning_rate=1., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=False, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# > Compute reconstruction of samples on learned dictionary
total_reconstruction_b_bis = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Csb[i], Cdictb_bis, p=None, q=None, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction_b_bis += reconstruction
np.testing.assert_allclose(total_reconstruction_b_bis, total_reconstruction_b, atol=1e-05)
np.testing.assert_allclose(Cdict_bis, nx.to_numpy(Cdictb_bis), atol=1e-03)
# Test: Perform same comparison without providing the initial dictionary being an optional input
# and testing other optimization settings untested until now.
# We pass previously estimated dictionaries to speed up the process.
use_adam_optimizer = False
verbose = True
use_log = True
np.random.seed(0)
Cdict_bis2, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Cs, D=n_atoms, nt=shape, ps=ps, q=q, Cdict_init=Cdict,
epochs=epochs, batch_size=n_samples, learning_rate=10., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=use_log, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# > Compute reconstruction of samples on learned dictionary
total_reconstruction_bis2 = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Cs[i], Cdict_bis2, p=ps[i], q=q, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction_bis2 += reconstruction
np.testing.assert_array_less(total_reconstruction_bis2, total_reconstruction)
# Test: Same after going through backend
np.random.seed(0)
Cdictb_bis2, log = ot.gromov.gromov_wasserstein_dictionary_learning(
Csb, D=n_atoms, nt=shape, ps=psb, q=qb, Cdict_init=Cdictb,
epochs=epochs, batch_size=n_samples, learning_rate=10., reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200,
projection=projection, use_log=use_log, use_adam_optimizer=use_adam_optimizer, verbose=verbose
)
# > Compute reconstruction of samples on learned dictionary
total_reconstruction_b_bis2 = 0
for i in range(n_samples):
_, _, _, reconstruction = ot.gromov.gromov_wasserstein_linear_unmixing(
Csb[i], Cdictb_bis2, p=psb[i], q=qb, reg=0.,
tol_outer=tol, tol_inner=tol, max_iter_outer=20, max_iter_inner=200
)
total_reconstruction_b_bis2 += reconstruction
np.testing.assert_allclose(total_reconstruction_b_bis2, total_reconstruction_bis2, atol=1e-05)
def test_fused_gromov_wasserstein_linear_unmixing(nx):
n = 10
X1, y1 = ot.datasets.make_data_classif('3gauss', n, random_state=42)
X2, y2 = ot.datasets.make_data_classif('3gauss2', n, random_state=42)
F, y = ot.datasets.make_data_classif('3gauss', n, random_state=42)
C1 = ot.dist(X1)
C2 = ot.dist(X2)
Cdict = np.stack([C1, C2])
Ydict = np.stack([F, F])
p = ot.unif(n)
C1b = nx.from_numpy(C1)
C2b = nx.from_numpy(C2)
Fb = nx.from_numpy(F)
Cdictb = nx.from_numpy(Cdict)
Ydictb = nx.from_numpy(Ydict)
pb = nx.from_numpy(p)
# Tests without regularization
reg = 0.
unmixing1, C1_emb, Y1_emb, OT, reconstruction1 = ot.gromov.fused_gromov_wasserstein_linear_unmixing(
C1, F, Cdict, Ydict, p=p, q=p, alpha=0.5, reg=reg,
tol_outer=10**(-6), tol_inner=10**(-6), max_iter_outer=20, max_iter_inner=200
)
unmixing1b, C1b_emb, Y1b_emb, OTb, reconstruction1b = ot.gromov.fused_gromov_wasserstein_linear_unmixing(
C1b, Fb, Cdictb, Ydictb, p=None, q=None, alpha=0.5, reg=reg,
tol_outer=10**(-6), tol_inner=10**(-6), max_iter_outer=20, max_iter_inner=200
)
unmixing2, C2_emb, Y2_emb, OT, reconstruction2 = ot.gromov.fused_gromov_wasserstein_linear_unmixing(
C2, F, Cdict, Ydict, p=None, q=None, alpha=0.5, reg=reg,
tol_outer=10**(-6), tol_inner=10**(-6), max_iter_outer=20, max_iter_inner=200
)