Probability Calibration of Classifiers in Scikit Learn

In this article, we will explore the concepts and techniques related to the probability calibration of classifiers in the context of machine learning. Classifiers in machine learning frequently provide probabilities indicating how confident they are in their predictions. However, the probabilities may not be well-calibrated. This means they do not accurately represent the true likelihood of the predicted class. To obtain well-calibrated probabilities, output probabilities are mapped through probability calibration. The Scikit-learn library includes techniques for improving classifier accuracy through probability calibration.

The process of determining how accurately the classification model's estimated probabilities correspond to the actual probabilities of the events being predicted is known as probability calibration.

There are two common approaches to probability calibration in Scikit-learn:

1. Platt Scaling (Logistic Regression) method: Fitting a logistic regression model to the classifier's output probabilities is accomplished by this method. A calibrated probability mapping function from the original probabilities is established by using maximum likelihood estimation. With the assistance of logistic regression, Scikit-learn's CalibratedClassifierCV class facilitates probability calibration.
    
2. Isotonic Regression: The true probabilities are believed to be monotonically (mathematical concept where a function or sequence either consistently increases or consistently decreases) related to the original ones in this method. The classifier's output probabilities are fit with a non-parametric isotonic regression model. A function that increases monotonically is learned by this model to map the original probabilities to calibrated probabilities. Scikit learns Isotonic Regression class is useful for achieving isotonic calibration.

The command to install scikit-learn using pip is:

pip install scikit-learn

Example 1: In this code, we will binary classification problem to demonstrate probability calibration using Platt Scaling in scikit-learn.

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.calibration import CalibratedClassifierCV
import numpy as np

# Load the Iris dataset
iris = load_iris()
X = iris.data
y = iris.target

# Split the dataset into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train a logistic regression classifier
clf = LogisticRegression()
clf.fit(X_train, y_train)

# Create a calibrated classifier using Platt Scaling
calibrated_clf = CalibratedClassifierCV(clf, method='sigmoid')
calibrated_clf.fit(X_train, y_train)

# Make predictions on the testing set
y_proba = calibrated_clf.predict_proba(X_test)

# Print the predicted class labels and probabilities
print("Predicted Probabilities:\n",[np.argmax(prob) for prob in y_proba])

Output:

Predicted Probabilities:
 [2, 0, 2, 1, 2, 0, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0]

Explanation: Functions used in the above code are:

• load_iris(): to load the Iris dataset
• train_test_split():  to split the dataset into training and testing sets
• LogisticRegression(): as the base classifier
• CalibratedClassifierCV(): for probability calibration

iris dataset is first loaded and the features and target variables are assigned to X and Y, respectively. Next, the dataset is split into training and testing sets using the train_test_split function. Here, 80% of the data is used for training (X_train, y_train), and 20% is used for testing (X_test, y_test).

Now, calibrated_clf is been created, and the calibrated classifier is then trained using the training data. Next, predictions are made on the testing set using the calibrated classifier. The predicted probabilities for each class are stored in y_proba.

Finally, the predicted class labels and probabilities are printed. 

• predicted labels (y_pred) represent the class predictions for each sample in the testing set
• predicted probabilities (y_proba) show the probability estimates for each class

Probability Calibration curve for binary Classification

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.tree import DecisionTreeClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB
from sklearn.calibration import CalibratedClassifierCV
from sklearn.calibration import CalibrationDisplay
import matplotlib.pyplot as plt

# Load the Breast Cancer dataset
cancer = load_breast_cancer()
X = cancer.data
y = cancer.target

# Split the dataset into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Classifiers
svc = SVC()
tree = DecisionTreeClassifier()
log = LogisticRegression(C=0.5)
gnb = GaussianNB()
svc_sigmoid = CalibratedClassifierCV(svc, cv=3, method="sigmoid", ensemble=True)
tree_isotonic = CalibratedClassifierCV(tree, cv=3, method="isotonic", ensemble=True)
gnb_sigmoid = CalibratedClassifierCV(gnb, cv=3, method="sigmoid", ensemble=True)

classifiers = {
    "Logistic":log,
    "Naive Bayes" : gnb,
    "SVM + sigmoid": svc_sigmoid,
    "Decision Tree + Isotonic": tree_isotonic,
    "Naive Bayes + Sigmoid" : gnb_sigmoid
}

# Plot Probability Calibration curve for each classifier
fig, ax = plt.subplots(figsize=(7, 5), dpi=150)
ax.plot([0, 1], [0, 1], linestyle='--', color='gray')

for name, clf in classifiers.items():
    clf.fit(X_train, y_train)
    clf_disp = CalibrationDisplay.from_estimator(clf, X_test, y_test, n_bins=10, name=name, ax=ax)

plt.title('Probability Calibration Curve')
plt.legend(loc="best")
plt.show()

Output:

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