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exp1_hypercube.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
###########################################################
# Experiment to estimate PRW mean error on hypercube data
###########################################################
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import pickle
from PRW import ProjectionRobustWasserstein
from Optimization.riemann_adap import RiemmanAdaptive
def T(x, d, dim=2):
assert dim <= d
assert dim >= 1
assert dim == int(dim)
return x + 2 * np.sign(x) * np.array(dim * [1] + (d - dim) * [0])
def fragmented_hypercube(n, d, dim):
assert dim <= d
assert dim >= 1
assert dim == int(dim)
a = (1. / n) * np.ones(n)
b = (1. / n) * np.ones(n)
# First measure : uniform on the hypercube
X = np.random.uniform(-1, 1, size=(n, d))
# Second measure : fragmentation
Y = T(np.random.uniform(-1, 1, size=(n, d)), d, dim)
return a, b, X, Y
d = 30 # Total dimension
k = 2 # k* = 2 and compute SRW with k = 2
nb_exp = 100 # Do 100 experiments
ns = [25, 50, 100, 250, 500, 1000] # Compute SRW between measures with 'n' points for 'n' in 'ns'
values = np.zeros((2, len(ns), nb_exp))
values_subspace = np.zeros((2, len(ns), nb_exp))
proj = np.zeros((d, d)) # Real optimal subspace
proj[0, 0] = 1
proj[1, 1] = 1
np.random.seed(357)
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)
# Riemann Gradient
algo = RiemmanAdaptive(reg=0.2, step_size_0=None, max_iter=30, threshold=1e-3,
max_iter_sinkhorn=30,
threshold_sinkhorn=1e-03, use_gpu=False)
PRW = ProjectionRobustWasserstein(X, Y, a, b, algo, k)
Omega, pi, maxmin_values = PRW.run(0, lr=0.01, beta=None)
values[0, indn, t] = np.abs(8 - PRW.get_value())
values_subspace[0, indn, t] = np.linalg.norm(Omega - proj)
# Riemann Adaptive Gradient
algo = RiemmanAdaptive(reg=0.2, step_size_0=None, max_iter=30, threshold=1e-3,
max_iter_sinkhorn=30,
threshold_sinkhorn=1e-03, use_gpu=False)
PRW = ProjectionRobustWasserstein(X, Y, a, b, algo, k)
Omega, pi, maxmin_values = PRW.run(1, lr=0.01, beta=0.8)
values[1, indn, t] = np.abs(8 - PRW.get_value())
values_subspace[1, indn, t] = np.linalg.norm(Omega - proj)
print('(RG) n =', n, '/', np.mean(values[0, indn, :]), np.mean(values_subspace[0, indn, :]))
print('(RAG) n =', n, '/', np.mean(values[1, indn, :]), np.mean(values_subspace[1, indn, :]))
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)
captions = ['PRW (RGAS)', 'PRW (RAGAS)']
plt.figure(figsize=(12, 8))
for t in range(2):
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, 'o-', 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', fontsize=25)
plt.ylabel('$|W^2(\mu,\\nu) - P_2^2(\hat\mu, \hat\\nu)|$', 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, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.5, 2.0]), 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(2):
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, 'o-', 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', 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')
# plt.close()
plt.show()