From 0afd84d744a472903d427e3c7ae32e55fdd7b9a7 Mon Sep 17 00:00:00 2001
From: Rémi Flamary <remi.flamary@gmail.com>
Date: Mon, 4 Apr 2022 10:23:04 +0200
Subject: [WIP] Add backend dual loss and plan computation for stochastic
 optimization or regularized OT (#360)

* add losses and plan computations and exmaple for dual oiptimization

* pep8

* add nice exmaple

* update awesome example stochasti dual

* add all tests

* pep8 + speedup exmaple

* add release info
---
 examples/backends/plot_dual_ot_pytorch.py | 168 ++++++++++++++++++++++++++++++
 1 file changed, 168 insertions(+)
 create mode 100644 examples/backends/plot_dual_ot_pytorch.py

(limited to 'examples/backends/plot_dual_ot_pytorch.py')

diff --git a/examples/backends/plot_dual_ot_pytorch.py b/examples/backends/plot_dual_ot_pytorch.py
new file mode 100644
index 0000000..d3f7a66
--- /dev/null
+++ b/examples/backends/plot_dual_ot_pytorch.py
@@ -0,0 +1,168 @@
+# -*- 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 te 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 teh 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 te 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')
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