Probability calibration in ML Python

Introduction

Probability calibration helps make sure the chances predicted by a model match real-world outcomes. It makes predictions more trustworthy and easier to understand.

When you want the predicted probabilities to reflect true chances, like in medical diagnosis.

When combining predictions from different models that output probabilities.

When making decisions based on risk, such as loan approvals or weather forecasts.

When evaluating models that output probabilities and you want to improve their reliability.

When the model tends to be overconfident or underconfident in its predictions.

Syntax

ML Python

from sklearn.calibration import CalibratedClassifierCV

calibrated_model = CalibratedClassifierCV(base_estimator=model, method='sigmoid', cv='prefit')
calibrated_model.fit(X_calibration, y_calibration)

# To predict calibrated probabilities:
probs = calibrated_model.predict_proba(X_test)

base_estimator is the original model you want to calibrate.

method can be 'sigmoid' (Platt scaling) or 'isotonic' (a non-parametric method).

Examples

Calibrating a logistic regression model using sigmoid method with a separate calibration set.

ML Python

from sklearn.linear_model import LogisticRegression
from sklearn.calibration import CalibratedClassifierCV

model = LogisticRegression()
model.fit(X_train, y_train)

calibrated = CalibratedClassifierCV(base_estimator=model, method='sigmoid', cv='prefit')
calibrated.fit(X_calibration, y_calibration)

probs = calibrated.predict_proba(X_test)

Calibrating a random forest using isotonic method with cross-validation on training data.

ML Python

from sklearn.ensemble import RandomForestClassifier
from sklearn.calibration import CalibratedClassifierCV

rf = RandomForestClassifier()
rf.fit(X_train, y_train)

calibrated_rf = CalibratedClassifierCV(base_estimator=rf, method='isotonic', cv=5)
calibrated_rf.fit(X_train, y_train)

probs = calibrated_rf.predict_proba(X_test)

Sample Model

This program trains a random forest, calibrates its predicted probabilities using a separate calibration set, and compares predicted probabilities before and after calibration. It also prints calibration curve points to see how close predicted probabilities are to true outcomes.

ML Python

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestClassifier
from sklearn.calibration import CalibratedClassifierCV, calibration_curve
import matplotlib.pyplot as plt

# Create a simple binary classification dataset
X, y = make_classification(n_samples=1000, n_features=20, random_state=42)

# Split data into train, calibration, and test sets
X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size=0.4, random_state=42)
X_calib, X_test, y_calib, y_test = train_test_split(X_temp, y_temp, test_size=0.5, random_state=42)

# Train a random forest classifier
rf = RandomForestClassifier(random_state=42)
rf.fit(X_train, y_train)

# Calibrate the classifier using sigmoid method and calibration set
calibrated_rf = CalibratedClassifierCV(base_estimator=rf, method='sigmoid', cv='prefit')
calibrated_rf.fit(X_calib, y_calib)

# Predict probabilities before and after calibration
probs_uncalibrated = rf.predict_proba(X_test)[:, 1]
probs_calibrated = calibrated_rf.predict_proba(X_test)[:, 1]

# Calculate calibration curves
prob_true_uncal, prob_pred_uncal = calibration_curve(y_test, probs_uncalibrated, n_bins=10)
prob_true_cal, prob_pred_cal = calibration_curve(y_test, probs_calibrated, n_bins=10)

# Print first 5 predicted probabilities before and after calibration
print('First 5 predicted probabilities before calibration:', probs_uncalibrated[:5])
print('First 5 predicted probabilities after calibration:', probs_calibrated[:5])

# Print calibration curve points
print('Calibration curve points before calibration:', list(zip(prob_pred_uncal, prob_true_uncal)))
print('Calibration curve points after calibration:', list(zip(prob_pred_cal, prob_true_cal)))

Important Notes

Calibration works best when you have a separate calibration dataset or use cross-validation.

Isotonic calibration can overfit if the calibration set is small.

Calibrated probabilities help in making better decisions when probabilities matter, not just class labels.

Summary

Probability calibration adjusts model outputs to better match true chances.

Use calibration when you need reliable probability estimates for decisions.

Common methods include sigmoid (Platt scaling) and isotonic regression.

Practice

1. What is the main goal of probability calibration in machine learning?

easy

A. To adjust predicted probabilities to better reflect true likelihoods

B. To increase the accuracy of class labels

C. To reduce the size of the training dataset

D. To speed up the training process

Solution

1. Step 1: Understand the purpose of probability calibration

   Probability calibration aims to make predicted probabilities match the actual chance of an event happening.

2. Step 2: Differentiate from accuracy and training speed

   Accuracy relates to correct labels, not probability quality. Calibration focuses on probability quality, not dataset size or speed.

3. Final Answer:

   To adjust predicted probabilities to better reflect true likelihoods -> Option A

4. Quick Check:

   Calibration = Adjust probabilities [OK]

Hint: Calibration fixes probability quality, not accuracy or speed [OK]

Common Mistakes:

• Confusing calibration with accuracy improvement
• Thinking calibration changes dataset size
• Assuming calibration speeds training

2. Which of the following is a common method used for probability calibration?

easy

A. K-means clustering

B. Gradient boosting

C. Platt scaling

D. Principal component analysis

Solution

1. Step 1: Identify calibration methods

   Platt scaling is a sigmoid-based method commonly used to calibrate probabilities.

2. Step 2: Exclude unrelated methods

   Gradient boosting is a model training technique, K-means is clustering, and PCA is dimensionality reduction, none are calibration methods.

3. Final Answer:

   Platt scaling -> Option C

4. Quick Check:

   Calibration method = Platt scaling [OK]

Hint: Remember Platt scaling for calibration, others are different tasks [OK]

Common Mistakes:

• Confusing boosting with calibration
• Mixing clustering or PCA with calibration
• Choosing any popular ML method as calibration

3. Given the following Python code using scikit-learn, what will be the output of calibrated_clf.predict_proba([[0.5, 1.5]])?

from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.calibration import CalibratedClassifierCV

X, y = make_classification(n_samples=100, n_features=2, random_state=42)
clf = LogisticRegression().fit(X, y)
calibrated_clf = CalibratedClassifierCV(clf, method='sigmoid', cv='prefit')
calibrated_clf.fit(X, y)

probs = calibrated_clf.predict_proba([[0.5, 1.5]])
print(probs)

medium

A. A 2D array with calibrated probabilities for each class, e.g. [[0.3, 0.7]]

B. A single float value representing probability

C. An error because cv='prefit' requires a different fit method

D. A list of predicted class labels, e.g. [1]

Solution

1. Step 1: Understand CalibratedClassifierCV output

   Using method='sigmoid' with cv='prefit' fits calibration on the existing model and outputs probabilities as a 2D array for each class.

2. Step 2: Check predict_proba output format

   predict_proba returns probabilities for each class in a 2D array, not a single float or labels.

3. Final Answer:

   A 2D array with calibrated probabilities for each class, e.g. [[0.3, 0.7]] -> Option A

4. Quick Check:

   predict_proba output = 2D array [OK]

Hint: predict_proba always returns 2D array of class probabilities [OK]

Common Mistakes:

• Expecting a single float instead of array
• Confusing predict_proba with predict
• Misunderstanding cv='prefit' usage

4. You tried to calibrate a classifier using CalibratedClassifierCV with cv=5, but got an error: "ValueError: Expected cv split to be a cross-validation generator or an iterable, got int instead." What is the likely cause?

medium

A. You passed cv=5 but the dataset has fewer than 5 samples

B. You passed an integer instead of a cross-validation splitter object

C. You used an unsupported calibration method

D. You forgot to fit the base classifier before calibration

Solution

1. Step 1: Analyze the error message

   The error "Expected cv split to be a cross-validation generator or an iterable, got int instead." directly points to the cv parameter receiving an integer (5) where a splitter was expected.

2. Step 2: Check CalibratedClassifierCV cv usage

   This occurs when cv is passed as int but the context requires an explicit cross-validation object like StratifiedKFold(5).

3. Step 3: Rule out unrelated causes

   Base fitting (D) is for cv='prefit'; dataset size (B) or method (C) don't trigger this error.

4. Final Answer:

   You passed an integer instead of a cross-validation splitter object -> Option B

5. Quick Check:

   Error 'got int instead' = cv type mismatch [OK]

Hint: cv requires cross-validation generator or iterable, not plain int [OK]

Common Mistakes:

• Passing an integer to cv instead of a splitter object
• Confusing cv parameter usage
• Assuming calibration method causes error

5. You have a binary classifier that outputs probabilities but they are poorly calibrated. You want to improve calibration on a small dataset without losing model accuracy. Which approach is best?

hard

A. Discard probabilities and use only predicted labels

B. Retrain the model with more epochs to improve accuracy

C. Use isotonic regression calibration on a separate validation set

D. Apply Platt scaling calibration using cross-validation

Solution

1. Step 1: Consider calibration methods for small datasets

   Platt scaling (sigmoid) is preferred for small datasets because it is less prone to overfitting than isotonic regression.

2. Step 2: Use cross-validation to avoid losing accuracy

   Applying Platt scaling with cross-validation calibrates probabilities without retraining the base model or losing accuracy.

3. Step 3: Evaluate other options

   Isotonic regression may overfit small data, retraining may not fix calibration, discarding probabilities loses useful info.

4. Final Answer:

   Apply Platt scaling calibration using cross-validation -> Option D

5. Quick Check:

   Small data calibration = Platt scaling + CV [OK]

Hint: For small data, prefer Platt scaling with CV for calibration [OK]

Common Mistakes:

• Using isotonic regression on small data causing overfit
• Retraining model instead of calibrating
• Ignoring probability calibration importance