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Least Ambiguous Set-Valued Classifiers with Bounded Error Levels, Sadinle et al. (2019)¶
We use SplitConformalClassifier to reproduce
Example 7 from Sadinle et al. (2019).
We consider a two-dimensional dataset with three labels. The distribution
of the data is a bivariate normal with diagonal covariance matrices for
each label.
We model the data with Gaussian Naive Bayes classifier
GaussianNB as a base model.
Prediction sets are estimated by
SplitConformalClassifier from the distribution of the
softmax scores of the true labels for three confidence level values (0.8, 0.9, and 0.95)
giving different class coverage levels.
When the class coverage level is not large enough, the prediction sets can be empty. This happens because the model is uncertain at the border between two labels. These so-called null regions disappear for larger coverage levels.
import matplotlib.pyplot as plt
import numpy as np
from sklearn.naive_bayes import GaussianNB
from mapie.classification import SplitConformalClassifier
# Create training set from multivariate normal distribution
centers = [(0, 3.5), (-2, 0), (2, 0)]
# covs = [[[1, 0], [0, 1]], [[2, 0], [0, 2]], [[5, 0], [0, 1]]]
covs = [np.eye(2), np.eye(2) * 2, np.diag([5, 1])]
x_min, x_max, y_min, y_max, step = -6, 8, -6, 8, 0.1
n_samples = 500
n_classes = 3
confidence_level = [0.8, 0.9, 0.95]
np.random.seed(42)
X_train = np.vstack(
[
np.random.multivariate_normal(center, cov, n_samples)
for center, cov in zip(centers, covs)
]
)
y_train = np.hstack([np.full(n_samples, i) for i in range(n_classes)])
# Create test from (x, y) coordinates
xx, yy = np.meshgrid(np.arange(x_min, x_max, step), np.arange(x_min, x_max, step))
X_test = np.stack([xx.ravel(), yy.ravel()], axis=1)
# Apply SplitConformalClassifier on the dataset to get prediction sets
clf = GaussianNB()
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
y_pred_proba = clf.predict_proba(X_test)
y_pred_proba_max = np.max(y_pred_proba, axis=1)
mapie = SplitConformalClassifier(
estimator=clf,
confidence_level=confidence_level,
prefit=True,
conformity_score="lac",
)
mapie.conformalize(X_train, y_train)
y_pred_mapie, y_ps_mapie = mapie.predict_set(X_test)
# Plot the results
tab10 = plt.cm.get_cmap("Purples", 4)
colors = {0: "#1f77b4", 1: "#ff7f0e", 2: "#2ca02c", 3: "#d62728"}
y_pred_col = list(map(colors.get, y_pred_mapie))
y_train_col = list(map(colors.get, y_train))
y_train_col = [colors[int(i)] for _, i in enumerate(y_train)]
fig, axs = plt.subplots(1, 4, figsize=(20, 4))
axs[0].scatter(
X_test[:, 0], X_test[:, 1], color=y_pred_col, marker=".", s=10, alpha=0.4
)
axs[0].scatter(
X_train[:, 0],
X_train[:, 1],
color=y_train_col,
marker="o",
s=10,
edgecolor="k",
)
axs[0].set_title("Predicted labels")
for i, confidence_level_ in enumerate(confidence_level):
y_ps_sums = y_ps_mapie[:, :, i].sum(axis=1)
num_labels = axs[i + 1].scatter(
X_test[:, 0],
X_test[:, 1],
c=y_ps_sums,
marker=".",
s=10,
alpha=1,
cmap=tab10,
vmin=0,
vmax=3,
)
cbar = plt.colorbar(num_labels, ax=axs[i + 1])
axs[i + 1].set_title(f"Number of labels for confidence_level={confidence_level_}")
plt.show()
Total running time of the script: ( 0 minutes 0.970 seconds)
Download Python source code: plot_sadinle2019_example.py