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"""
==========================
Stochastic test
==========================
This example is designed to test the stochatic optimization algorithms module
for descrete and semicontinous measures from the POT library.
"""
# Authors: Kilian Fatras <kilian.fatras@gmail.com>
# Rémi Flamary <remi.flamary@polytechnique.edu>
#
# License: MIT License
import numpy as np
import ot
#############################################################################
# COMPUTE TEST FOR SEMI-DUAL PROBLEM
#############################################################################
#############################################################################
#
# TEST SAG algorithm
# ---------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_stochastic_sag():
# test sag
n = 10
reg = 1
numItermax = 30000
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G = ot.stochastic.solve_semi_dual_entropic(
u, u, M, reg, "sag", numItermax=numItermax
)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-03) # cf convergence sag
np.testing.assert_allclose(u, G.sum(0), atol=1e-03) # cf convergence sag
#############################################################################
#
# TEST ASGD algorithm
# ---------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_stochastic_asgd():
# test asgd
n = 10
reg = 1
numItermax = 10000
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G, log = ot.stochastic.solve_semi_dual_entropic(
u, u, M, reg, "asgd", numItermax=numItermax, log=True
)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-02) # cf convergence asgd
np.testing.assert_allclose(u, G.sum(0), atol=1e-02) # cf convergence asgd
#############################################################################
#
# TEST Convergence SAG and ASGD toward Sinkhorn's solution
# --------------------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a learning rate and a number of iteration
def test_sag_asgd_sinkhorn():
# test all algorithms
n = 10
reg = 1
nb_iter = 10000
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G_asgd = ot.stochastic.solve_semi_dual_entropic(
u, u, M, reg, "asgd", numItermax=nb_iter
)
G_sag = ot.stochastic.solve_semi_dual_entropic(
u, u, M, reg, "sag", numItermax=nb_iter
)
G_sinkhorn = ot.sinkhorn(u, u, M, reg)
# check constraints
np.testing.assert_allclose(G_sag.sum(1), G_sinkhorn.sum(1), atol=1e-02)
np.testing.assert_allclose(G_sag.sum(0), G_sinkhorn.sum(0), atol=1e-02)
np.testing.assert_allclose(G_asgd.sum(1), G_sinkhorn.sum(1), atol=1e-02)
np.testing.assert_allclose(G_asgd.sum(0), G_sinkhorn.sum(0), atol=1e-02)
np.testing.assert_allclose(G_sag, G_sinkhorn, atol=1e-02) # cf convergence sag
np.testing.assert_allclose(G_asgd, G_sinkhorn, atol=1e-02) # cf convergence asgd
#############################################################################
# COMPUTE TEST FOR DUAL PROBLEM
#############################################################################
#############################################################################
#
# TEST SGD algorithm
# ---------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a batch_size and a number of iteration
def test_stochastic_dual_sgd():
# test sgd
n = 10
reg = 1
numItermax = 5000
batch_size = 10
rng = np.random.RandomState(0)
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G, log = ot.stochastic.solve_dual_entropic(
u, u, M, reg, batch_size, numItermax=numItermax, log=True
)
# check constraints
np.testing.assert_allclose(u, G.sum(1), atol=1e-03) # cf convergence sgd
np.testing.assert_allclose(u, G.sum(0), atol=1e-03) # cf convergence sgd
#############################################################################
#
# TEST Convergence SGD toward Sinkhorn's solution
# --------------------------------------------------------
# 2 identical discrete measures u defined on the same space with a
# regularization term, a batch_size and a number of iteration
def test_dual_sgd_sinkhorn():
# test all dual algorithms
n = 10
reg = 1
nb_iter = 5000
batch_size = 10
rng = np.random.RandomState(0)
# Test uniform
x = rng.randn(n, 2)
u = ot.utils.unif(n)
M = ot.dist(x, x)
G_sgd = ot.stochastic.solve_dual_entropic(
u, u, M, reg, batch_size, numItermax=nb_iter
)
G_sinkhorn = ot.sinkhorn(u, u, M, reg)
# check constraints
np.testing.assert_allclose(G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-02)
np.testing.assert_allclose(G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-02)
np.testing.assert_allclose(G_sgd, G_sinkhorn, atol=1e-02) # cf convergence sgd
# Test gaussian
n = 30
reg = 1
batch_size = 30
a = ot.datasets.make_1D_gauss(n, 15, 5) # m= mean, s= std
b = ot.datasets.make_1D_gauss(n, 15, 5)
X_source = np.arange(n, dtype=np.float64)
Y_target = np.arange(n, dtype=np.float64)
M = ot.dist(X_source.reshape((n, 1)), Y_target.reshape((n, 1)))
M /= M.max()
G_sgd = ot.stochastic.solve_dual_entropic(
a, b, M, reg, batch_size, numItermax=nb_iter
)
G_sinkhorn = ot.sinkhorn(a, b, M, reg)
# check constraints
np.testing.assert_allclose(G_sgd.sum(1), G_sinkhorn.sum(1), atol=1e-03)
np.testing.assert_allclose(G_sgd.sum(0), G_sinkhorn.sum(0), atol=1e-03)
np.testing.assert_allclose(G_sgd, G_sinkhorn, atol=1e-03) # cf convergence sgd
def test_loss_dual_entropic(nx):
nx.seed(0)
xs = nx.randn(50, 2)
xt = nx.randn(40, 2) + 2
ws = nx.rand(50)
ws = ws / nx.sum(ws)
wt = nx.rand(40)
wt = wt / nx.sum(wt)
u = nx.randn(50)
v = nx.randn(40)
def metric(x, y):
return -nx.dot(x, y.T)
ot.stochastic.loss_dual_entropic(u, v, xs, xt)
ot.stochastic.loss_dual_entropic(u, v, xs, xt, ws=ws, wt=wt, metric=metric)
def test_plan_dual_entropic(nx):
nx.seed(0)
xs = nx.randn(50, 2)
xt = nx.randn(40, 2) + 2
ws = nx.rand(50)
ws = ws / nx.sum(ws)
wt = nx.rand(40)
wt = wt / nx.sum(wt)
u = nx.randn(50)
v = nx.randn(40)
def metric(x, y):
return -nx.dot(x, y.T)
G1 = ot.stochastic.plan_dual_entropic(u, v, xs, xt)
assert np.all(nx.to_numpy(G1) >= 0)
assert G1.shape[0] == 50
assert G1.shape[1] == 40
G2 = ot.stochastic.plan_dual_entropic(u, v, xs, xt, ws=ws, wt=wt, metric=metric)
assert np.all(nx.to_numpy(G2) >= 0)
assert G2.shape[0] == 50
assert G2.shape[1] == 40
def test_loss_dual_quadratic(nx):
nx.seed(0)
xs = nx.randn(50, 2)
xt = nx.randn(40, 2) + 2
ws = nx.rand(50)
ws = ws / nx.sum(ws)
wt = nx.rand(40)
wt = wt / nx.sum(wt)
u = nx.randn(50)
v = nx.randn(40)
def metric(x, y):
return -nx.dot(x, y.T)
ot.stochastic.loss_dual_quadratic(u, v, xs, xt)
ot.stochastic.loss_dual_quadratic(u, v, xs, xt, ws=ws, wt=wt, metric=metric)
def test_plan_dual_quadratic(nx):
nx.seed(0)
xs = nx.randn(50, 2)
xt = nx.randn(40, 2) + 2
ws = nx.rand(50)
ws = ws / nx.sum(ws)
wt = nx.rand(40)
wt = wt / nx.sum(wt)
u = nx.randn(50)
v = nx.randn(40)
def metric(x, y):
return -nx.dot(x, y.T)
G1 = ot.stochastic.plan_dual_quadratic(u, v, xs, xt)
assert np.all(nx.to_numpy(G1) >= 0)
assert G1.shape[0] == 50
assert G1.shape[1] == 40
G2 = ot.stochastic.plan_dual_quadratic(u, v, xs, xt, ws=ws, wt=wt, metric=metric)
assert np.all(nx.to_numpy(G2) >= 0)
assert G2.shape[0] == 50
assert G2.shape[1] == 40
|
