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# -*- coding: utf-8 -*-
r"""
======================================================================
Continuous OT plan estimation with Pytorch
======================================================================
"""
# Author: Remi Flamary <remi.flamary@polytechnique.edu>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 3
import numpy as np
import matplotlib.pyplot as pl
import torch
from torch import nn
import ot
import ot.plot
# %%
# Data generation
# ---------------
torch.manual_seed(42)
np.random.seed(42)
n_source_samples = 1000
n_target_samples = 1000
theta = 2 * np.pi / 20
noise_level = 0.1
Xs = np.random.randn(n_source_samples, 2) * 0.5
Xt = np.random.randn(n_target_samples, 2) * 2
# one of the target mode changes its variance (no linear mapping)
Xt = Xt + 4
# %%
# Plot data
# ---------
nvisu = 300
pl.figure(1, (5, 5))
pl.clf()
pl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker="+", label="Source samples", alpha=0.5)
pl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker="o", label="Target samples", alpha=0.5)
pl.legend(loc=0)
ax_bounds = pl.axis()
pl.title("Source and target distributions")
# %%
# Convert data to torch tensors
# -----------------------------
xs = torch.tensor(Xs)
xt = torch.tensor(Xt)
# %%
# Estimating deep dual variables for entropic OT
# ----------------------------------------------
torch.manual_seed(42)
# define the MLP model
class Potential(torch.nn.Module):
def __init__(self):
super(Potential, self).__init__()
self.fc1 = nn.Linear(2, 200)
self.fc2 = nn.Linear(200, 1)
self.relu = torch.nn.ReLU() # instead of Heaviside step fn
def forward(self, x):
output = self.fc1(x)
output = self.relu(output) # instead of Heaviside step fn
output = self.fc2(output)
return output.ravel()
u = Potential().double()
v = Potential().double()
reg = 1
optimizer = torch.optim.Adam(list(u.parameters()) + list(v.parameters()), lr=0.005)
# number of iteration
n_iter = 500
n_batch = 500
losses = []
for i in range(n_iter):
# generate noise samples
iperms = torch.randint(0, n_source_samples, (n_batch,))
ipermt = torch.randint(0, n_target_samples, (n_batch,))
xsi = xs[iperms]
xti = xt[ipermt]
# minus because we maximize the dual loss
loss = -ot.stochastic.loss_dual_entropic(u(xsi), v(xti), xsi, xti, reg=reg)
losses.append(float(loss.detach()))
if i % 10 == 0:
print("Iter: {:3d}, loss={}".format(i, losses[-1]))
loss.backward()
optimizer.step()
optimizer.zero_grad()
pl.figure(2)
pl.plot(losses)
pl.grid()
pl.title("Dual objective (negative)")
pl.xlabel("Iterations")
# %%
# Plot the density on target for a given source sample
# ----------------------------------------------------
nv = 100
xl = np.linspace(ax_bounds[0], ax_bounds[1], nv)
yl = np.linspace(ax_bounds[2], ax_bounds[3], nv)
XX, YY = np.meshgrid(xl, yl)
xg = np.concatenate((XX.ravel()[:, None], YY.ravel()[:, None]), axis=1)
wxg = np.exp(-((xg[:, 0] - 4) ** 2 + (xg[:, 1] - 4) ** 2) / (2 * 2))
wxg = wxg / np.sum(wxg)
xg = torch.tensor(xg)
wxg = torch.tensor(wxg)
pl.figure(4, (12, 4))
pl.clf()
pl.subplot(1, 3, 1)
iv = 2
Gg = ot.stochastic.plan_dual_entropic(
u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg
)
Gg = Gg.reshape((nv, nv)).detach().numpy()
pl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker="+", zorder=2, alpha=0.05)
pl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker="o", zorder=2, alpha=0.05)
pl.scatter(
Xs[iv : iv + 1, 0],
Xs[iv : iv + 1, 1],
s=100,
marker="+",
label="Source sample",
zorder=2,
alpha=1,
color="C0",
)
pl.pcolormesh(XX, YY, Gg, cmap="Greens", label="Density of transported source sample")
pl.legend(loc=0)
ax_bounds = pl.axis()
pl.title("Density of transported source sample")
pl.subplot(1, 3, 2)
iv = 3
Gg = ot.stochastic.plan_dual_entropic(
u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg
)
Gg = Gg.reshape((nv, nv)).detach().numpy()
pl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker="+", zorder=2, alpha=0.05)
pl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker="o", zorder=2, alpha=0.05)
pl.scatter(
Xs[iv : iv + 1, 0],
Xs[iv : iv + 1, 1],
s=100,
marker="+",
label="Source sample",
zorder=2,
alpha=1,
color="C0",
)
pl.pcolormesh(XX, YY, Gg, cmap="Greens", label="Density of transported source sample")
pl.legend(loc=0)
ax_bounds = pl.axis()
pl.title("Density of transported source sample")
pl.subplot(1, 3, 3)
iv = 6
Gg = ot.stochastic.plan_dual_entropic(
u(xs[iv : iv + 1, :]), v(xg), xs[iv : iv + 1, :], xg, reg=reg, wt=wxg
)
Gg = Gg.reshape((nv, nv)).detach().numpy()
pl.scatter(Xs[:nvisu, 0], Xs[:nvisu, 1], marker="+", zorder=2, alpha=0.05)
pl.scatter(Xt[:nvisu, 0], Xt[:nvisu, 1], marker="o", zorder=2, alpha=0.05)
pl.scatter(
Xs[iv : iv + 1, 0],
Xs[iv : iv + 1, 1],
s=100,
marker="+",
label="Source sample",
zorder=2,
alpha=1,
color="C0",
)
pl.pcolormesh(XX, YY, Gg, cmap="Greens", label="Density of transported source sample")
pl.legend(loc=0)
ax_bounds = pl.axis()
pl.title("Density of transported source sample")
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