Expected Model Change

Note

The generated animation can be found at the bottom of the page.

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 scipy.stats import uniform

from skactiveml.utils import MISSING_LABEL, labeled_indices, is_labeled

from skactiveml.regressor import NICKernelRegressor
from skactiveml.pool import ExpectedModelChangeMaximization

random_state = np.random.RandomState(0)


def true_function(X_):
    return (X_**3 + 2 * X_**2 + X_ - 1).flatten()

n_samples = 100
X = np.concatenate(
        [uniform.rvs(0, 1.5, 9 * n_samples // 10, random_state=random_state),
         uniform.rvs(1.5, 0.5, n_samples // 10, random_state=random_state)]
    ).reshape(-1, 1)

noise = np.vectorize(lambda x : random_state.rand() * 1.5 if x < 1
                                else random_state.rand() * 0.5)

# Build a dataset.
y_true = true_function(X) + noise(X).flatten()
y = np.full(shape=y_true.shape, fill_value=MISSING_LABEL)
X_test = np.linspace(0, 2, num=100).reshape(-1, 1)

# Initialise the regressor.
reg = NICKernelRegressor(random_state=random_state, metric_dict={'gamma': 15.0})
# Initialise the query strategy.
qs = ExpectedModelChangeMaximization()


# Preparation for plotting.
fig, (ax_1, ax_2) = plt.subplots(2, 1, sharex=True)
artists = []

# The active learning cycle:
n_cycles = 20
for c in range(n_cycles):
    # Fit the classifier.
    reg.fit(X, y)

    # Get labeled instances.
    X_labeled = X[labeled_indices(y)]

    # Query the next instance/s.
    query_idx = qs.query(X=X, y=y, reg=reg)

    # Plot the labeled data.
    coll_old = list(ax_1.collections) + list(ax_2.collections)
    title = ax_1.text(
        0.5,
        1.05,
        f"Prediction after acquring {c} labels",
        size=plt.rcParams["axes.titlesize"],
        ha="center",
        transform=ax_1.transAxes,
    )

    _, utilities_test = qs.query(
        X=X, y=y, reg=reg, candidates=X_test, return_utilities=True
    )

    utilities_test = (utilities_test - utilities_test.min()).flatten()
    if np.any(utilities_test != utilities_test[0]):
        utilities_test /= utilities_test.max()

    is_lbld = is_labeled(y)

    (utility_line,) = ax_2.plot(X_test, utilities_test, c="green")
    utility_fill = plt.fill_between(
        X_test.flatten(), utilities_test, color="green", alpha=0.3
    )

    ax_1.scatter(X[~is_lbld], y_true[~is_lbld], c="lightblue")
    ax_1.scatter(X[is_lbld], y[is_lbld], c="orange")

    y_pred = reg.predict(X_test)
    (prediction_line,) = ax_1.plot(X_test, y_pred, c="black")

    coll_new = list(ax_1.collections) + list(ax_2.collections)
    coll_new.append(title)
    artists.append(
        [x for x in coll_new if (x not in coll_old)]
        + [utility_line, utility_fill, prediction_line]
    )

    # Label the queried instances.
    y[query_idx] = y_true[query_idx]

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

Once Loop Reflect

References:

The implementation of this strategy is based on Cai et al.1.

1

Wenbin Cai, Ya Zhang, and Jun Zhou. Maximizing expected model change for active learning in regression. In 2013 IEEE 13th international conference on data mining, 51–60. IEEE, 2013.