forked from moreo/QuaPy
203 lines
6.5 KiB
Python
203 lines
6.5 KiB
Python
"""
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This example shows how to use Bayesian quantification (https://arxiv.org/abs/2302.09159),
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which is suitable for low-data situations and when the uncertainty of the prevalence estimate is of interest.
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For this, we will need to install extra dependencies:
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```
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$ pip install quapy[bayesian]
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```
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Running the script via:
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```
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$ python examples/bayesian_quantification.py
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```
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will produce a plot `bayesian_quantification.pdf`.
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Due to a low sample size and the fact that classes 2 and 3 are hard to distinguish,
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it is hard to estimate the proportions accurately, what is visible by looking at the posterior samples,
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showing large uncertainty.
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"""
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from dataclasses import dataclass
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn.ensemble import RandomForestClassifier
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from quapy.method.aggregative import BayesianCC, ACC, PACC
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from quapy.data import LabelledCollection
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FIGURE_PATH = "bayesian_quantification.pdf"
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@dataclass
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class SimulatedData:
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"""Auxiliary class to keep the training and test data sets."""
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n_classes: int
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X_train: np.ndarray
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Y_train: np.ndarray
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X_test: np.ndarray
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Y_test: np.ndarray
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def simulate_data(rng) -> SimulatedData:
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"""Generates a simulated data set with three classes."""
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# Number of examples of each class in both data sets
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n_train = [400, 400, 400]
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n_test = [40, 25, 15]
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# Mean vectors and shared covariance of P(X|Y) distributions
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mus = [np.zeros(2), np.array([1, 1.5]), np.array([1.5, 1])]
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cov = np.eye(2)
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# Generate the features accordingly
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X_train = np.concatenate([
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rng.multivariate_normal(mus[i], cov, size=n_train[i])
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for i in range(3)
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])
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X_test = np.concatenate([
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rng.multivariate_normal(mus[i], cov, size=n_test[i])
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for i in range(3)
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])
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Y_train = np.concatenate([[i] * n for i, n in enumerate(n_train)])
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Y_test = np.concatenate([[i] * n for i, n in enumerate(n_test)])
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return SimulatedData(
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n_classes=3,
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X_train=X_train,
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X_test=X_test,
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Y_train=Y_train,
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Y_test=Y_test,
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)
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def plot_simulated_data(axs, data: SimulatedData) -> None:
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"""Plots a simulated data set.
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Args:
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axs: a list of three `plt.Axes` objects, on which the samples will be plotted.
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data: the simulated data set.
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"""
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xlim = (
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-0.3 + min(data.X_train[:, 0].min(), data.X_test[:, 0].min()),
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0.3 + max(data.X_train[:, 0].max(), data.X_test[:, 0].max())
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)
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ylim = (
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-0.3 + min(data.X_train[:, 1].min(), data.X_test[:, 1].min()),
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0.3 + max(data.X_train[:, 1].max(), data.X_test[:, 1].max())
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)
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for ax in axs:
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ax.set_xlabel("$X_1$")
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ax.set_ylabel("$X_2$")
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ax.set_aspect("equal")
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ax.set_xlim(*xlim)
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ax.set_ylim(*ylim)
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ax.set_xticks([])
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ax.set_yticks([])
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ax = axs[0]
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ax.set_title("Training set")
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for i in range(data.n_classes):
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ax.scatter(data.X_train[data.Y_train == i, 0], data.X_train[data.Y_train == i, 1], c=f"C{i}", s=3, rasterized=True)
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ax = axs[1]
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ax.set_title("Test set\n(with labels)")
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for i in range(data.n_classes):
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ax.scatter(data.X_test[data.Y_test == i, 0], data.X_test[data.Y_test == i, 1], c=f"C{i}", s=3, rasterized=True)
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ax = axs[2]
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ax.set_title("Test set\n(as observed)")
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ax.scatter(data.X_test[:, 0], data.X_test[:, 1], c="C5", s=3, rasterized=True)
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def get_random_forest() -> RandomForestClassifier:
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"""An auxiliary factory method to generate a random forest."""
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return RandomForestClassifier(n_estimators=10, random_state=5)
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def train_and_plot_bayesian_quantification(ax: plt.Axes, training: LabelledCollection, test: np.ndarray, n_classes: int) -> None:
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"""Fits Bayesian quantification and plots posterior mean as well as individual samples"""
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quantifier = BayesianCC(classifier=get_random_forest())
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quantifier.fit(training)
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# Obtain mean prediction
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mean_prediction = quantifier.quantify(test)
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x_ax = np.arange(n_classes)
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ax.plot(x_ax, mean_prediction, c="salmon", linewidth=2, linestyle=":", label="Bayesian")
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# Obtain individual samples
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samples = quantifier.get_prevalence_samples()
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for sample in samples[::5, :]:
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ax.plot(x_ax, sample, c="salmon", alpha=0.1, linewidth=0.3, rasterized=True)
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def _get_estimate(estimator_class, training: LabelledCollection, test: np.ndarray) -> None:
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"""Auxiliary method for running ACC and PACC."""
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estimator = estimator_class(get_random_forest())
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estimator.fit(training)
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return estimator.quantify(test)
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def train_and_plot_acc(ax: plt.Axes, training: LabelledCollection, test: np.ndarray, n_classes: int) -> None:
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estimate = _get_estimate(ACC, training, test)
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ax.plot(np.arange(n_classes), estimate, c="darkblue", linewidth=2, linestyle=":", label="ACC")
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def train_and_plot_pacc(ax: plt.Axes, training: LabelledCollection, test: np.ndarray, n_classes: int) -> None:
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estimate = _get_estimate(PACC, training, test)
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ax.plot(np.arange(n_classes), estimate, c="limegreen", linewidth=2, linestyle=":", label="PACC")
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def plot_true_proportions(ax: plt.Axes, test_labels: np.ndarray, n_classes: int) -> None:
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"""Plots the true proportions."""
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counts = np.bincount(test_labels, minlength=n_classes)
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proportion = counts / counts.sum()
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x_ax = np.arange(n_classes)
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ax.plot(x_ax, proportion, c="black", linewidth=2, label="True")
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ax.set_xlabel("Class")
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ax.set_ylabel("Prevalence")
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ax.set_xticks(x_ax, x_ax + 1)
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ax.set_yticks([0, 0.25, 0.5, 0.75, 1.0])
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ax.set_xlim(-0.1, n_classes - 0.9)
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ax.set_ylim(-0.01, 1.01)
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def main() -> None:
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# --- Simulate data ---
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rng = np.random.default_rng(42)
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data = simulate_data(rng)
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# --- Plot simulated data ---
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fig, axs = plt.subplots(1, 4, figsize=(13, 3), dpi=300)
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for ax in axs:
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ax.spines[['top', 'right']].set_visible(False)
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plot_simulated_data(axs[:3], data)
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# --- Plot quantification results ---
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ax = axs[3]
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plot_true_proportions(ax, test_labels=data.Y_test, n_classes=data.n_classes)
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training = LabelledCollection(data.X_train, data.Y_train)
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train_and_plot_acc(ax, training=training, test=data.X_test, n_classes=data.n_classes)
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train_and_plot_pacc(ax, training=training, test=data.X_test, n_classes=data.n_classes)
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train_and_plot_bayesian_quantification(ax=ax, training=training, test=data.X_test, n_classes=data.n_classes)
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ax.legend(bbox_to_anchor=(1.05, 1), loc='upper left', frameon=False)
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fig.tight_layout()
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fig.savefig(FIGURE_PATH)
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if __name__ == '__main__':
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main()
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