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# -*- coding: utf-8 -*-
r"""
======================================================================
Dual OT solvers for entropic and quadratic regularized OT 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
import ot
import ot.plot
# %%
# Data generation
# ---------------
torch.manual_seed(1)
n_source_samples = 100
n_target_samples = 100
theta = 2 * np.pi / 20
noise_level = 0.1
Xs, ys = ot.datasets.make_data_classif("gaussrot", n_source_samples, nz=noise_level)
Xt, yt = ot.datasets.make_data_classif(
"gaussrot", n_target_samples, theta=theta, nz=noise_level
)
# one of the target mode changes its variance (no linear mapping)
Xt[yt == 2] *= 3
Xt = Xt + 4
# %%
# Plot data
# ---------
pl.figure(1, (10, 5))
pl.clf()
pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples")
pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples")
pl.legend(loc=0)
pl.title("Source and target distributions")
# %%
# Convert data to torch tensors
# -----------------------------
xs = torch.tensor(Xs)
xt = torch.tensor(Xt)
# %%
# Estimating dual variables for entropic OT
# -----------------------------------------
u = torch.randn(n_source_samples, requires_grad=True)
v = torch.randn(n_source_samples, requires_grad=True)
reg = 0.5
optimizer = torch.optim.Adam([u, v], lr=1)
# number of iteration
n_iter = 200
losses = []
for i in range(n_iter):
# generate noise samples
# minus because we maximize the dual loss
loss = -ot.stochastic.loss_dual_entropic(u, v, xs, xt, 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")
Ge = ot.stochastic.plan_dual_entropic(u, v, xs, xt, reg=reg)
# %%
# Plot the estimated entropic OT plan
# -----------------------------------
pl.figure(3, (10, 5))
pl.clf()
ot.plot.plot2D_samples_mat(Xs, Xt, Ge.detach().numpy(), alpha=0.1)
pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples", zorder=2)
pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples", zorder=2)
pl.legend(loc=0)
pl.title("Source and target distributions")
# %%
# Estimating dual variables for quadratic OT
# ------------------------------------------
u = torch.randn(n_source_samples, requires_grad=True)
v = torch.randn(n_source_samples, requires_grad=True)
reg = 0.01
optimizer = torch.optim.Adam([u, v], lr=1)
# number of iteration
n_iter = 200
losses = []
for i in range(n_iter):
# generate noise samples
# minus because we maximize the dual loss
loss = -ot.stochastic.loss_dual_quadratic(u, v, xs, xt, 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(4)
pl.plot(losses)
pl.grid()
pl.title("Dual objective (negative)")
pl.xlabel("Iterations")
Gq = ot.stochastic.plan_dual_quadratic(u, v, xs, xt, reg=reg)
# %%
# Plot the estimated quadratic OT plan
# ------------------------------------
pl.figure(5, (10, 5))
pl.clf()
ot.plot.plot2D_samples_mat(Xs, Xt, Gq.detach().numpy(), alpha=0.1)
pl.scatter(Xs[:, 0], Xs[:, 1], marker="+", label="Source samples", zorder=2)
pl.scatter(Xt[:, 0], Xt[:, 1], marker="o", label="Target samples", zorder=2)
pl.legend(loc=0)
pl.title("OT plan with quadratic regularization")
|
