Bayesian Active Learning by Disagreement (BALD)#

Idea: BALD reduces the number of possible hypotheses maximally fast to minimize the uncertainty about the parameters using Shannon’s entropy. It seeks the data point that maximises the decrease in expected posterior entropy. For the batch case, a greedy (top-k) selection is applied.

Google Colab Note: If the notebook fails to run after installing the needed packages, try to restart the runtime (Ctrl + M) under Runtime -> Restart session.

Notebook Dependencies

Uncomment the following cell to install all dependencies for this tutorial.

# !pip install scikit-activeml

import numpy as np
from matplotlib import pyplot as plt, animation
from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split

from skactiveml.utils import MISSING_LABEL, labeled_indices
from skactiveml.visualization import plot_utilities, plot_decision_boundary

from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.ensemble import BaggingClassifier
from skactiveml.classifier import SklearnClassifier
from skactiveml.pool import GreedyBALD
from skactiveml.utils import unlabeled_indices

random_state = np.random.RandomState(0)

# Build a dataset.
X_true, y_clusters = make_blobs(
    n_samples=400,
    n_features=2,
    centers=[[0, 1], [-3, 0.5], [-1, -1], [2, 1], [1, -0.5]],
    cluster_std=0.7,
    random_state=random_state,
)
y_true = y_clusters % 2

X_pool, X_test, y_pool, y_test = train_test_split(
    X_true, y_true, test_size=0.25, random_state=random_state
)

X = X_pool
y = np.full(shape=y_pool.shape, fill_value=MISSING_LABEL)

# Initialise the classifier.
clf = SklearnClassifier(BaggingClassifier(
    SklearnClassifier(GaussianProcessClassifier(), random_state=random_state),
    random_state=random_state),
    classes=np.unique(y_true),
    random_state=random_state
)

# Initialise the query strategy.
qs = GreedyBALD(random_state=random_state)

# Preparation for plotting.
fig, ax = plt.subplots()
feature_bound = [
    [min(X[:, 0]), min(X[:, 1])],
    [max(X[:, 0]), max(X[:, 1])]
]
artists = []

# Active learning cycle:
n_cycles = 20
for c in range(n_cycles):
    # Fit the classifier with current labels.
    clf.fit(X, y)

    # Query the next sample(s).
    query_idx = qs.query(X=X, y=y, ensemble=clf)

    # Capture the current plot state.
    coll_old = list(ax.collections)
    title = ax.text(
        0.5, 1.05,
        f"Decision boundary after acquiring {c} labels\n"
        f"Test Accuracy: {clf.score(X_test, y_test):.4f}",
        size=plt.rcParams["axes.titlesize"],
        ha="center", transform=ax.transAxes,
    )

    # Update plot with utility values, samples, and decision boundary.
    X_labeled = X[labeled_indices(y)]
    ax = plot_utilities(
        qs,
        X=X, y=y, ensemble=clf,
        replace_nan=None, candidates=X[unlabeled_indices(y)],
        res=25,
        feature_bound=feature_bound,
        ax=ax,
    )
    ax.scatter(
        X[:, 0],
        X[:, 1],
        c=y_pool,
        cmap="coolwarm",
        marker=".",
        zorder=2
    )
    ax.scatter(
        X_labeled[:, 0],
        X_labeled[:, 1],
        c="grey",
        alpha=0.8,
        marker=".",
        s=300,
    )
    ax = plot_decision_boundary(clf, feature_bound, ax=ax)
    ax.set_xlabel('Feature 1')
    ax.set_ylabel('Feature 2')

    coll_new = list(ax.collections)
    coll_new.append(title)
    artists.append([x for x in coll_new if x not in coll_old])

    # Update labels based on query.
    y[query_idx] = y_pool[query_idx]

ani = animation.ArtistAnimation(fig, artists, interval=1000, blit=True)

../../../_images/pool_classification_legend1.png

References:

The implementation of this strategy is based on Houlsby et al.[1].

Total running time of the script: (0 minutes 10.804 seconds)

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Bayesian Active Learning by Disagreement (BALD)#

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