def main():
d = 20 # Total dimension
k = 2 # k* = 2 and compute SRW with k = 2
nb_exp = 100 # Do 500 experiments
ns = [25, 50, 100, 250, 500,
1000] # Compute SRW between measures with 'n' points for 'n' in 'ns'
values = np.zeros((3, len(ns), nb_exp))
values_subspace = np.zeros((3, len(ns), nb_exp))
proj = np.zeros((d, d)) # Real optimal subspace
proj[0, 0] = 1
proj[1, 1] = 1
eta = 0.2
tau = 0.001
verb = True
if 1 == 1:
for indn in range(len(ns)):
n = ns[indn]
# Sample nb_exp times
for t in range(nb_exp):
a, b, X, Y = fragmented_hypercube(n, d, dim=2)
U0 = np.zeros((d, k))
U0[:k, :] = np.eye(k)
algo = RiemannianBlockCoordinateDescent(eta=eta,
tau=None,
max_iter=3000,
threshold=0.1,
verbose=verb)
PRW = ProjectedRobustWasserstein(X, Y, a, b, algo, k)
PRW.run('RBCD', tau, U0)
values[0, indn, t] = np.abs(8 - PRW.get_value())
values_subspace[0, indn,
t] = np.linalg.norm(PRW.get_Omega() - proj)
algo1 = RiemannianGradientAscentSinkhorn(eta=eta,
tau=None,
max_iter=3000,
threshold=0.1,
sink_threshold=1e-4,
verbose=verb)
PRW1 = ProjectedRobustWasserstein(X, Y, a, b, algo1, k)
PRW1.run('RGAS', tau / eta, U0)
values[1, indn, t] = np.abs(8 - PRW1.get_value())
values_subspace[1, indn,
t] = np.linalg.norm(PRW1.get_Omega() - proj)
# Compute Wasserstein
algo2 = ProjectedGradientAscent(reg=eta,
step_size_0=tau,
max_iter=1,
max_iter_sinkhorn=50,
threshold=0.001,
threshold_sinkhorn=1e-04,
use_gpu=False)
W_ = SubspaceRobustWasserstein(X, Y, a, b, algo2, k=d)
W_.run()
values[2, indn, t] = np.abs(8 - W_.get_value())
values_subspace[2, indn,
t] = np.linalg.norm(W_.get_Omega() - proj)
print(W_.get_value())
with open('./results/exp1_hypercube_value.pkl', 'wb') as f:
pickle.dump([values, values_subspace], f)
else:
with open('./results/exp1_hypercube_value.pkl', 'rb') as f:
values, values_subspace = pickle.load(f)
print('n =', n, '/', np.mean(values[indn, :]), '/',
np.mean(values1[indn, :]))
captions = ['PRW (RBCD)', 'PRW (RGAS)']
line = ['o-', 'o--', '-']
plt.figure(figsize=(12, 8))
for t in range(3):
values_mean = np.mean(values[t, :, :], axis=1)
values_min = np.min(values[t, :, :], axis=1)
values_10 = np.percentile(values[t, :, :], 10, axis=1)
values_25 = np.percentile(values[t, :, :], 25, axis=1)
values_75 = np.percentile(values[t, :, :], 75, axis=1)
values_90 = np.percentile(values[t, :, :], 90, axis=1)
values_max = np.max(values[t, :, :], axis=1)
mean, = plt.semilogy(ns,
values_mean,
line[t],
lw=4,
ms=11,
label=captions[t])
col = mean.get_color()
plt.fill_between(ns, values_25, values_75, facecolor=col, alpha=0.3)
plt.fill_between(ns, values_10, values_90, facecolor=col, alpha=0.2)
plt.xlabel('Number of points n', fontsize=25)
plt.ylabel('MEE', fontsize=25)
plt.legend(loc='best', fontsize=25)
plt.title('Mean estimation error', fontsize=30)
plt.xticks(ns, fontsize=20)
plt.yticks(np.array([0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0]), fontsize=20)
plt.gca().xaxis.set_major_formatter(ticker.FormatStrFormatter('%0.0f'))
plt.gca().yaxis.set_major_formatter(ticker.FormatStrFormatter('%0.1f'))
plt.grid(ls=':')
plt.savefig('figs/exp1_hypercube_value_1.png')
plt.show()
plt.close()
plt.clf()
plt.figure(figsize=(12, 8))
for t in range(3):
values_subspace_mean = np.mean(values_subspace[t, :, :], axis=1)
values_subspace_min = np.min(values_subspace[t, :, :], axis=1)
values_subspace_10 = np.percentile(values_subspace[t, :, :],
10,
axis=1)
values_subspace_25 = np.percentile(values_subspace[t, :, :],
25,
axis=1)
values_subspace_75 = np.percentile(values_subspace[t, :, :],
75,
axis=1)
values_subspace_90 = np.percentile(values_subspace[t, :, :],
90,
axis=1)
values_subspace_max = np.max(values_subspace[t, :, :], axis=1)
mean, = plt.loglog(ns,
values_subspace_mean,
line[t],
lw=4,
ms=11,
label=captions[t])
col = mean.get_color()
plt.fill_between(ns,
values_subspace_25,
values_subspace_75,
facecolor=col,
alpha=0.3)
plt.fill_between(ns,
values_subspace_10,
values_subspace_90,
facecolor=col,
alpha=0.2)
plt.fill_between(ns,
values_subspace_min,
values_subspace_max,
facecolor=col,
alpha=0.15)
plt.xlabel('Number of points n', fontsize=25)
plt.ylabel('$||\Omega^* - \widehat\Omega||_F$', fontsize=25)
plt.legend(loc='best', fontsize=25)
plt.title('Mean subspace estimation error', fontsize=30)
plt.xticks(ns, fontsize=20)
plt.yticks(np.array(range(1, 8)) / 10, fontsize=20)
plt.gca().xaxis.set_major_formatter(ticker.FormatStrFormatter('%0.0f'))
plt.gca().yaxis.set_major_formatter(ticker.FormatStrFormatter('%0.1f'))
plt.grid(ls=':')
plt.savefig('figs/exp1_hypercube_value_2.png')
for indn in range(len(ns)):
n = ns[indn]
# Sample nb_exp times
for t in range(nb_exp):
FW = FrankWolfe(reg=0.2,
step_size_0=None,
max_iter=15,
threshold=0.01,
max_iter_sinkhorn=30,
threshold_sinkhorn=10e-04,
use_gpu=False)
a, b, X, Y = disk_annulus(n, d, dim=2)
SRW_FW = SubspaceRobustWasserstein(X, Y, a, b, FW, k)
SRW_FW.run()
values[indn, t] = np.abs(REAL_VALUE - SRW_FW.get_value())
values_subspace[indn, t] = cp.linalg.norm(SRW_FW.get_Omega() - proj)
print('n =', n, '/', np.mean(values[indn, :]))
values_mean = np.mean(values, axis=1)
values_min = np.min(values, axis=1)
values_10 = np.percentile(values, 10, axis=1)
values_25 = np.percentile(values, 25, axis=1)
values_75 = np.percentile(values, 75, axis=1)
values_90 = np.percentile(values, 90, axis=1)
values_max = np.max(values, axis=1)
import matplotlib.ticker as ticker
plt.figure(figsize=(17, 6))
mean, = plt.loglog(ns, values_mean, 'o-', lw=4, ms=11)
col = mean.get_color()