Multi-domain Linear Monge Alignment

This example illustrates the use of the MultiLinearMongeAlignmentAdapter

# Author: Remi Flamary
#
# License: BSD 3-Clause
# sphinx_gallery_thumbnail_number = 4

import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import LogisticRegression

from skada import (
    MultiLinearMongeAlignmentAdapter,
    make_da_pipeline,
    source_target_split,
)
from skada.datasets import make_shifted_datasets

Generate concept drift classification dataset and plot it

We generate a simple 2D concept drift dataset.

X, y, sample_domain = make_shifted_datasets(
    n_samples_source=20,
    n_samples_target=20,
    shift="concept_drift",
    noise=0.2,
    label="multiclass",
    random_state=42,
)


Xs, Xt, ys, yt = source_target_split(X, y, sample_domain=sample_domain)


plt.figure(5, (10, 5))
plt.subplot(1, 2, 1)
plt.scatter(Xs[:, 0], Xs[:, 1], c=ys, cmap="tab10", vmax=9, label="Source")
plt.title("Source data")
ax = plt.axis()

plt.subplot(1, 2, 2)
plt.scatter(Xt[:, 0], Xt[:, 1], c=yt, cmap="tab10", vmax=9, label="Target")
plt.title("Target data")
plt.axis(ax)

(np.float64(-2.3676169789533272), np.float64(4.53817259426296), np.float64(-1.7964573229829714), np.float64(4.336863129384494))

Train a classifier on source data

We train a simple SVC classifier on the source domain and evaluate its performance on the source and target domain. Performance is much lower on the target domain due to the shift. We also plot the decision boundary

clf = MultiLinearMongeAlignmentAdapter()
clf.fit(X, sample_domain=sample_domain)

X_adapt = clf.transform(X, sample_domain=sample_domain, allow_source=True)


plt.figure(5, (10, 3))
plt.subplot(1, 3, 1)
plt.scatter(Xs[:, 0], Xs[:, 1], c=ys, cmap="tab10", vmax=9, label="Source")
plt.title("Source data")
ax = plt.axis()

plt.subplot(1, 3, 2)
plt.scatter(Xt[:, 0], Xt[:, 1], c=yt, cmap="tab10", vmax=9, label="Target")
plt.title("Target data")
plt.axis(ax)

plt.subplot(1, 3, 3)
plt.scatter(
    X_adapt[sample_domain >= 0, 0],
    X_adapt[sample_domain >= 0, 1],
    c=y[sample_domain >= 0],
    marker="o",
    cmap="tab10",
    vmax=9,
    label="Source",
    alpha=0.5,
)
plt.scatter(
    X_adapt[sample_domain < 0, 0],
    X_adapt[sample_domain < 0, 1],
    c=y[sample_domain < 0],
    marker="x",
    cmap="tab10",
    vmax=9,
    label="Target",
    alpha=1,
)
plt.legend()
plt.title("Adapted data")

Text(0.5, 1.0, 'Adapted data')

Train a classifier on adapted data

clf = make_da_pipeline(
    MultiLinearMongeAlignmentAdapter(),
    LogisticRegression(),
)

clf.fit(X, y, sample_domain=sample_domain)

print(
    "Average accuracy on all domains:",
    clf.score(X, y, sample_domain=sample_domain, allow_source=True),
)

Average accuracy on all domains: 0.9875

def get_multidomain_data(
    n_samples_source=100,
    n_samples_target=100,
    noise=0.1,
    random_state=None,
    n_sources=3,
    n_targets=2,
):
    np.random.seed(random_state)
    X, y, sample_domain = make_shifted_datasets(
        n_samples_source=n_samples_source,
        n_samples_target=n_samples_target,
        noise=noise,
        shift="concept_drift",
        label="multiclass",
        random_state=random_state,
    )
    for ns in range(n_sources - 1):
        Xi, yi, sample_domaini = make_shifted_datasets(
            n_samples_source=n_samples_source,
            n_samples_target=n_samples_target,
            noise=noise,
            shift="concept_drift",
            label="multiclass",
            random_state=random_state + ns,
            mean=np.random.randn(2),
            sigma=np.random.rand(2) * 0.5 + 0.5,
        )
        Xs, Xt, ys, yt = source_target_split(Xi, yi, sample_domain=sample_domaini)
        X = np.vstack([X, Xt])
        y = np.hstack([y, yt])
        sample_domain = np.hstack([sample_domain, np.ones(Xt.shape[0]) * (ns + 2)])

    for nt in range(n_targets - 1):
        Xi, yi, sample_domaini = make_shifted_datasets(
            n_samples_source=n_samples_source,
            n_samples_target=n_samples_target,
            noise=noise,
            shift="concept_drift",
            label="multiclass",
            random_state=random_state + nt + 42,
            mean=np.random.randn(2),
            sigma=np.random.rand(2) * 0.5 + 0.5,
        )
        Xs, Xt, ys, yt = source_target_split(Xi, yi, sample_domain=sample_domaini)
        X = np.vstack([X, Xt])
        y = np.hstack([y, yt])
        sample_domain = np.hstack([sample_domain, -np.ones(Xt.shape[0]) * (nt + 1)])

    return X, y, sample_domain


X, y, sample_domain = get_multidomain_data(
    n_samples_source=50,
    n_samples_target=50,
    noise=0.1,
    random_state=43,
    n_sources=3,
    n_targets=2,
)

Xs, Xt, ys, yt = source_target_split(X, y, sample_domain=sample_domain)


plt.figure(5, (10, 5))
plt.subplot(1, 2, 1)
plt.scatter(Xs[:, 0], Xs[:, 1], c=ys, cmap="tab10", vmax=9, label="Source")
plt.title("Source data")
ax = plt.axis()

plt.subplot(1, 2, 2)
plt.scatter(Xt[:, 0], Xt[:, 1], c=yt, cmap="tab10", vmax=9, label="Target")
plt.title("Target domains")
plt.axis(ax)

(np.float64(-2.310098338155625), np.float64(4.756925382279493), np.float64(-2.1443686989830857), np.float64(4.464886123797522))

clf = MultiLinearMongeAlignmentAdapter()
clf.fit(X, sample_domain=sample_domain)

X_adapt = clf.transform(X, sample_domain=sample_domain, allow_source=True)


plt.figure(5, (10, 3))
plt.subplot(1, 3, 1)
plt.scatter(Xs[:, 0], Xs[:, 1], c=ys, cmap="tab10", vmax=9, label="Source")
plt.title("Source data")
ax = plt.axis()

plt.subplot(1, 3, 2)
plt.scatter(Xt[:, 0], Xt[:, 1], c=yt, cmap="tab10", vmax=9, label="Target")
plt.title("Target data")
plt.axis(ax)

plt.subplot(1, 3, 3)
plt.scatter(
    X_adapt[sample_domain >= 0, 0],
    X_adapt[sample_domain >= 0, 1],
    c=y[sample_domain >= 0],
    marker="o",
    cmap="tab10",
    vmax=9,
    label="Source",
    alpha=0.5,
)
plt.scatter(
    X_adapt[sample_domain < 0, 0],
    X_adapt[sample_domain < 0, 1],
    c=y[sample_domain < 0],
    marker="x",
    cmap="tab10",
    vmax=9,
    label="Target",
    alpha=1,
)
plt.legend()
plt.axis(ax)
plt.title("Adapted data")

Text(0.5, 1.0, 'Adapted data')

Train a classifier on adapted data

clf = make_da_pipeline(
    MultiLinearMongeAlignmentAdapter(),
    LogisticRegression(),
)

clf.fit(X, y, sample_domain=sample_domain)

print(
    "Average accuracy on all domains:",
    clf.score(X, y, sample_domain=sample_domain, allow_source=True),
)

Average accuracy on all domains: 1.0