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Diffstat (limited to 'examples/backends')
-rw-r--r-- | examples/backends/plot_dual_ot_pytorch.py | 168 | ||||
-rw-r--r-- | examples/backends/plot_stoch_continuous_ot_pytorch.py | 189 |
2 files changed, 357 insertions, 0 deletions
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') diff --git a/examples/backends/plot_stoch_continuous_ot_pytorch.py b/examples/backends/plot_stoch_continuous_ot_pytorch.py new file mode 100644 index 0000000..6d9b916 --- /dev/null +++ b/examples/backends/plot_stoch_continuous_ot_pytorch.py @@ -0,0 +1,189 @@ +# -*- 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 = 10000 +n_target_samples = 10000 +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=.005) + +# number of iteration +n_iter = 1000 +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 te 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 arget 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 sourec 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 sourec 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 sourec sample') +pl.legend(loc=0) +ax_bounds = pl.axis() +pl.title('Density of transported source sample') |