Improved Greedy Sampling (GSi)

Idea: Improved Greedy Sampling (GSi) at first selects those samples that maximize the diversity in the feature space and then selects samples to maximize the diversity in the combined space of features and targets. The diversity is maximized by selecting those samples that are the furthest away from all previously labeled samples. The distance in the combined space is measured as the product of the distance in the feature space and the target space. To measure the distance in the target space the strategy predicts the label corresponding to each unlabeled sample.

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, is_labeled

from skactiveml.regressor import NICKernelRegressor
from skactiveml.pool import GreedySamplingTarget

# Set a fixed random state for reproducibility.
random_state = np.random.RandomState(0)


def true_function(X_):
    """Compute the true underlying function."""
    return (X_**3 + 2 * X_**2 + X_ - 1).flatten()


# Generate samples.
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)

# Define noise: higher noise for X < 1 and lower otherwise.
noise = np.vectorize(
    lambda x: random_state.rand() * 1.5 if x < 1 else random_state.rand() * 0.5
)

# Build the 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)
y_test = true_function(X_test)

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

# Initialise the query strategy.
qs = GreedySamplingTarget(method='GSi')

# Prepare the plotting area.
fig, (ax_1, ax_2) = plt.subplots(2, 1, sharex=True)
artists = []

# Active learning cycle.
n_cycles = 20
for c in range(n_cycles):
    # Fit the regressor using the current labels.
    reg.fit(X, y)

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

    # Record current plot elements.
    coll_old = list(ax_1.collections) + list(ax_2.collections)
    title = ax_1.text(
        0.5, 1.05,
        f"Prediction after acquiring {c} labels\n"
        f"Test R-squared score: {reg.score(X_test, y_test):.4f}",
        size=plt.rcParams["axes.titlesize"],
        ha="center",
        transform=ax_1.transAxes,
    )
    ax_1.set_xlabel('Sample')
    ax_1.set_ylabel('Target Value')
    ax_2.set_xlabel('Sample')
    ax_2.set_ylabel('Utility')

    # Compute utility values for the test candidates.
    _, 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()

    # Plot utility information on the second axis.
    (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)

    # Plot the samples and their labels.
    is_lbld = is_labeled(y)
    ax_1.scatter(X[~is_lbld], y_true[~is_lbld], c="lightblue")
    ax_1.scatter(X[is_lbld], y[is_lbld], c="orange")

    # Predict and plot the regressor's output.
    y_pred = reg.predict(X_test)
    (prediction_line,) = ax_1.plot(X_test, y_pred, c="black")

    # Capture new plot elements.
    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]
    )

    # Update labels for the queried sample.
    y[query_idx] = y_true[query_idx]

# Create an animation from the collected frames.
ani = animation.ArtistAnimation(fig, artists, interval=1000, blit=True)

Once Loop Reflect

References:

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

[1]

Dongrui Wu, Chin-Teng Lin, and Jian Huang. Active Learning for Regression using Greedy Sampling. Inf. Sci., 474:90–105, 2019.